Bibliography

[Ada90] R. K. Adair. The Physics of Baseball. Harper and Row, New York, 1990.

[AF66] M. Athans and P. L. Falb. Optimal Control. An Introduction to the Theoryand its Applications. McGraw-Hill, New York, 1966.

[Agr89] G. P. Agrawal. Nonlinear Fiber Optics. Academic Press, New York, 1989.

[AH81] R. Axelrod and W. D. Hamilton. The evolution of cooperation. Science,211:1390, 1981.

[AJMS81] R. M. Anderson, H. C. Jackson, R. M. May, and A. M. Smith. Populationdynamics of fox rabies in Europe. Nature, 289:765, 1981.

[AL82] F. T. Arecchi and F. Lisi. Hopping mechanism generating 1/f noise innonlinear systems. Phys. Rev. Lett., 49:94, 1982.

[ALSB73] J. Aroesty, T. Lincoln, N. Shapiro, and G. Boccia. Tumor growth andchemotherapy: mathematical methods, computer simulations, and exper­imental foundations. Math. Biosc., 17:243, 1973.

[AM82] R. Anderson and R. May. The logic of vaccination. New Scientist, Novem­ber, 1982.

[AMMJ86] R. M. Anderson, G. F. Medley, R. M. May, and R. M. Johnson. A prelim­inary study of the transmission dynamics of the human immunodeficiencyvirus (HIV), the causative agent of AIDS. IMA J. Math. Appl. Med. Biol.,3:229, 1986.

[AMS+98] P. Avan, P. Magnan, J. Smyrzynski, R. Probst, and A. Dancer. Directevidence of cubic difference tone propagation by intercochlear acousticpressure measurements in the guinea-pig. Eur. J. Neurosci., 10:1764, 1998.

[AN86] Y. Aizawa and I. Nishikawa. Toward the classification of the patterns gen­erated by one-dimensional cell automata. In G. Ikegami, editor, DynamicalSystems and Nonlinear Oscillations. World Scientific, Singapore, 1986.

345

R. H. Enns, It’s a Nonlinear World, DOI 10.1007/978-0-387-75340-9,© Springer Science+Business Media, LLC 2011

346 BIBLIOGRAPHY

[And82] R. M. Anderson. Directly transmitted viral and bacterial infections of man.In R. M. Anderson, editor, Population Dynamics of Infectious Diseases,Theory and Applications. Chapman and Hall, New York, 1982.

[ANST86] S. V. Antipov, M. V. Nezlin, E. N. Snezhkin, and A. S. Trubnikov. Rossbyautosoliton and stationary model of the Jovian Great Red Spot. Nature,323:238, 1986.

[AR63] P. W. Anderson and J. M. Rowell. Probable observation of the Josephsonsuperconducting tunneling effect. Phys. Rev. Lett., 10:230, 1963.

[AS72] M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions(AMS 55). National Bureau of Standards, Washington, DC, 1972.

[ASKS07] T. Asai, K. Seo, O. Kobayashi, and R. Sakashita. Fundamental aerody­namics of the soccer ball. Sports Eng., 10:101, 2007.

[AW96] A. Aguzzi and C. Weissmann. Bovine spongiform encephalopathy: a sus­picious signature. Nature, 383:666, 1996.

[AW97] A. Aguzzi and C. Weissmann. Prion research: the next frontiers. Nature,389:795, 1997.

[AW98] A. Aguzzi and C. Weissmann. Spongiform encephalopathies: the prionsperplexing persistence. Nature, 392:763, 1998.

[Axe06] R. Axelrod. The Evolution of Cooperation (revised edition). Basic Books,New York, 2006.

[Bak95] G. Baker. Control of the chaotic driven pendulum. Am. J. Phys., 63:832,1995.

[Bar88] M. Barnsley. Fractals Everywhere. Academic Press, San Diego, 1988.

[Bas69] F. M. Bass. A new product growth model for consumer durables. Man­agement Science, 15:215, 1969.

[Bat67] G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge Univer­sity Press, Cambridge, 1967.

[BC74] G. W. Bluman and J. D. Cole. Similarity Methods for Differential Equa­tions. Springer-Verlag, New York, 1974.

[BC90] P. N. Butcher and D. Cotter. The Elements of Nonlinear Optics. Cam­bridge University Press, Cambridge, 1990.

[BCD02] N. Bellomo, V. Coscia, and M. Delitala. On the mathematical theory ofvehicular traffic flow I. Fluid dynamic and kinetic modelling. Math. ModelsMethods Appl. Sci., 12:1801, 2002.

BIBLIOGRAPHY 347

[BeaOO] D. H. Bearce. Economic sanctions and neural networks: forecasting effec­tiveness and re-considering cooperation. In Diana Richards, editor, Po­litical Complexity: Nonlinear Models of Politics. University of MichiganPress, Ann Arbor, 2000.

[BeI58] B. P. Belousov. Oscillation reaction and its mechanism. In Collection ofAbstracts on Radiation Medicine. Medgiz, Moscow, 1958.

[BEMS71] A. Barone, F. Esposito, C. J. Magee, and A. C. Scott. Theory and appli­cations of the sine-Gordon equation. Riv. Nuovo Cim., 1:227, 1971.

[BEP71] I. P. Batra, R. H. Enns, and D. Pohl. Stimulated thermal scattering oflight. Physica Status Solidi, (b) 48:11, 1971.

[Bet66] A. Betz. Introduction to the Theory of Flow Machines (D. G. Randall,Trans.). Pergamon Press, Oxford, 1966.

[BF89] R. L. Burden and J. D. Faires. Numerical Analysis. PWS-Kent PublishingCompany, Boston, 4th edition, 1989.

[BFW81] G. J. Butler, H. I. Freedman, and P. Waltman. Global dynamics of aselection model for the growth of a population with genotypic fertilitydifferences. J. Math. BioI., 12:25, 1981.

[BG91] Y. Braiman and I. Goldhirsch. Taming chaotic dynamics with weak peri­odic perturbations. Phys. Rev. Lett., 66:2545, 1991.

[BGD+09] J. C. Bohorquez, S. Gourley, A. R. Dixon, M. Spagat, and N. F. Johnson.Common ecology quantifies human insurgency. Nature, 462:911, 2009.

[BH80] J. J. Beaman and J. K. Hedrick. Freight car harmonic response: a sim­plified nonlinear method. In R. V. Ramnath, J. K. Hedrick, and H. M.Paynter, editors, Nonlinear System Analysis and Synthesis, Vol. 2. ASME,1980.

[BJ91] J. Bloxham and A. Jackson. Fluid flow near the surface of Earth's outercore. Rev. Geophys., 29:97, 1991.

[BJ92] J. Bloxham and A. Jackson. Time-dependent mapping of the magneticfield at the core-mantle boundary. J. Geophys. Res., 97:19537, 1992.

[BJ99] E. D. Brodie and E. D. Brodie Jr. Predator-prey arms races. Bioscience,49:557, 1999.

[BM63] G. M. Baule and R. McFee. Detection of the magnetic field of the heart.Am. Heart J., 66:95, 1963.

[BM82] J. R. Beddington and R. M. May. The harvesting of interacting species ina natural ecosystem. Sci. Am., November:62, 1982.

348

[BSG02]

[Buc77]

[BufOO]

[BZ98]

[Cam87]

[CCOl]

[CE80]

[CFL28]

[CFvN50]

[CH80]

[Cha39]

[Chr69]

[CHT97]

[Chu92]

[Chu94]

[Coh67]

BIBLIOGRAPHY

G. Bub, A. Shrier, and L. Glass. Spiral wave generation in heterogeneousexcitable media. Phys. Rev. Lett., 88:Feb. 4, 2002.

U. H. Buzzi, N. Stergiou, M. J. Kurz, P. A. Hageman, and J. Heidel.Nonlinear dynamics indicates aging affects variability during gait. Clin.Biomech., 18:435, 2003.

J. Buckmaster. Viscous sheets advancing over dry beds. J. Fluid Mech.,81:735, 1977.

B. A. Buffett. Earth's core and the geodynamo. Science, 288:2007, 2000.

M. R. Berenbaum and A. R. Zangerl. Chemical phenotype matchingbetween a plant and its insect herbivore. Proc. Natl. Acad. Sci. USA,95:13743, 1998.

D. Campbell. Nonlinear science-from paradigms to practicalities. LosAlamos Sci., 15:218, 1987.

P. S. Chen and P. Chu. Applying Lanchester's linear law to model theArdennes campaign. Naval Res. Logist., 8:653, 2001.

P. Collet and J. P. Eckmann. Iterated Maps of the Interval as DynamicalSystems. Birkhauser, Boston, 1980.

R. Courant, K. Friedrichs, and H. Lewy. Uber die partiellen differenzen­gleichungen der mathematischen physik. Math. Ann., 100:32, 1928.

J. G. Charney, R. Fj6rtoft, and J. von Neumann. Numerical integrationof the barotropic vorticity equation. Tellus, 2:237, 1950.

D. R. J. Chillingworth and R. J. Holmes. Dynamical systems and modelsfor reversals of the earth's magnetic field. Math. Ceol., 12:41, 1980.

S. Chandrasekhar. An Introduction to the Study of Stellar Structure. DoverReprint, Chicago, 1939.

M. Chrichton. The Andromeda Strain. Alfred A. Knopf, New York, 1969.

B. M. Clement, A. Holzheid, and A. Tilgner. Core geophysics. Proc. Natl.Acad. Sci. USA, 94(24):12472, 1997.

L. O. Chua. The genesis of Chua's circuit. Arch. Electron. Ubertragung­stechnik, 46:250, 1992.

L. O. Chua. Chua's circuit: an overview ten years later. J. Circuits Syst.Comput., 4:117, 1994.

D. Cohen. Magnetic fields around the torso: production by electricalactivity of the human heart. Science, 156:652, 1967.

BIBLIOGRAPHY 349

[Coh72]

[CoI51]

[Co080]

[Cro03]

[CSS92]

[CTS64]

[Cun64]

[Cvi84]

[Dav62]

[DCPS08]

[Dei62]

[Den98]

[Den03]

[Die75]

[DNS99]

D. Cohen. Magnetoencephalography: detection of the brain's electricalactivity with a superconducting magnetometer. Science, 175:664, 1972.

J. D. Cole. On a quasi-linear parabolic equation occurring in aerodynam­ics. Q. Appl. Math., 9:225, 1951.

N. K. Cooperrider. Nonlinear behavior in rail vehicle dynamics. InJ. Holmes, editor, New Approaches to Nonlinear Problems in Dynamics.SIAM, Philadelphia, 1980.

A. W. Crosby(Jr). America's Forgotten Pandemic: The Influenza of 1918(originally published in 1976 as Epidemic and Peace, 1918, by GreenwoodPress). Cambridge University Press, Cambridge, 2003.

J. J. Casciari, S. V. Sot irchos , and R. M. Sutherland. Mathematical mod­eling of microenvironment and growth in EMT6/Ro multicellular tumourspheroids. Cell Proliferation, 25:1, 1992.

R. Y. Chiao, C. H. Townes, and B. P. Stoicheff. Stimulated Brillouinscattering and coherent generation of intense hypersonic waves. Phys.Rev. Lett., 12:592, 1964.

W. J. Cunningham. Introduction to Nonlinear Analysis. McGraw Hill,New York, 1964.

P. Cvitanovic. Universality in Chaos. Adam Hilger, Bristol, 1984.

H. T. Davis. Introduction to Nonlinear Differential and Integral Equations.Dover, New York, 1962.

D. H. Douglass, J. R. Christy, B. D. Pearson, and S. F. Singer. A com­parison of tropical temperature trends with model predictions. Int. J.Climatol., 27:1519, 2008.

S. J. Deitchman. A Lanchester model of guerilla warfare. Oper. Res.,10:818, 1962.

M. Denny. Curling rock dynamics. Can. J. Phys., 76:295, 1998.

M. Denny. Comment on "The motion of a curling rock". Can. J. Phys.,81:877, 2003.

K. Dietz. Transmission and control of arborvirus diseases. In D. Lud­wig and K. L. Cooke, editors, Epidemiology, SIMS 1974 Utah ConferenceProceedings. SIAM, Philadelphia, 1975.

J. P. Dunne, E. Nikolaidou, and R. P. Smith. Arms race models and econo­metric applications. In The Arms Trade, Security and Conflict, Conferenceat Middlesex University Business School. Middlesex University BusinessSchool, 1999.

350

[Dra92]

BIBLIOGRAPHY

P. G. Drazin. Nonlinear Systems. Cambridge University Press, Cambridge,1992.

[DRS90] W. L. Ditto, S. N. Rauseo, and M. L. Spano. Experimental control ofchaos. Phys. Rev. Lett., 65:3211, 1990.

[dWKV+98] G. A. de Wijs, G. Kress, L. Vocadlo, D. Dobson, A. Alfe, M. J. Gillan,and G. D. Price. The viscosity of liquid iron at the physical conditions ofthe earth's core. Nature, 392:805, 1998.

[Ede61]

[EE95]

[Egg97]

M. Eden. A two-dimensional growth process. In J . Neyman, editor, Pro­ceedings of the Fourth Berkeley Symposium on Mathematical Statistics andProbability, Volume IV: Biology and Problems of Health. University of Cal­ifornia Press, Berkeley, 1961.

D. E. Edmundson and R. H. Enns. Particle-like nature of colliding 3­dimensional optical solitons. Phys. Rev. A, 51:2491, 1995.

J. Eggers. Nonlinear dynamics and breakup of free-surface flows. Rev.Mod. Phys., 69:865, 1997.

[EGSW081] M. Eigen, W. Gardiner, P. Schuster, and R. Winkler-Oswatitsch. Theorigin of genetic information. Scientific American, April:88, 1981.

[Eig71]

[EK88]

[EMOO]

[EM01]

[EM06]

[EM07]

[Emd07]

[Emm77]

M. Eigen. Self-organization of matter and evolution of biological macro­molecules. Die Naturrwissenschajten, 58:465, 1971.

L. Edelstein-Keshet. Mathematical Models in Biology. Random House,New York, 1988.

R. H. Enns and G. C. McGuire. Nonlinear Physics with Maple for Scien­tists and Engineers. Birkhauser, Boston, 2000.

R. H. Enns and G. C. McGuire. Nonlinear Physics with Mathematica forScientists and Engineers. Birkhauser, Boston, 2001.

R. H. Enns and G. C. McGuire. Computer Algebra Recipes: An Introduc­tory Guide to the Mathematical Models of Science. Springer, New York,2006.

R. H. Enns and G. C. McGuire. Computer Algebra Recipes: An AdvancedGuide to Scientific Modeling. Springer, New York, 2007.

R. Emden. Gaskugeln: Anwendungen der Mechanischen Wiirmetheorieauf Kosmologische und Meteorologische Probleme. B. G. Teubner, Berlin,1907.

G. S. Emmerson. John Scott Russell-A Great Victorian Engineer andNaval Architect. John Murray, London, 1977.

BIBLIOGRAPHY 351

[EMS88]

[Eng54]

[ENM89]

[ER79]

[Eva82]

[FC86]

[IDC87]

[Fea98]

[Fei79]

[Fei80]

[Fis37]

[Fit61]

[FKN72]

[FLS65]

[FN74]

[FPU65]

M. Eigen, John McCaskill, and Peter Schuster. Molecular quasi-species.J. Phys. Chem., 92:6881, 1988.

J. H. Engel. A verification of Lanchester's law. Opere Res., 2:163, 1954.

J. M. Elzebda, A. H. Nayfeh, and D. T. Mook. Development of an an­alytical model of wing rock for slender delta wings. J. Aircraft, 26:737,1989.

R. H. Enns and S. S. Rangnekar. The 3-wave interaction in nonlinearoptics. Physica Status Solidi, (b) 94:9, 1979.

A. S. Evans. Viral Infections of Humans, 2nd edition. Plenum MedicalBook Company, New York, 1982.

G. R. Fowles and G. L. Cassiday. Analytical Mechanics. Saunders CollegePublishing, Orlando, 1986.

U. S. Centers for Disease Control. Enterically transmitted non-A, non-Bhepatitus-East Africa. Morbidity and Mortality Weekly Report, 36:241,1987.

Physics World Features. The physics of football. Phys. World Mag., June1:25, 1998.

M. J. Feigenbaum. The universal metric properties of nonlinear transfor­mations. J. Stat. Phys., 21:69, 1979.

M. J. Feigenbaum. Universal behavior in nonlinear systems. Los AlamosSci., 1:4, 1980.

R. A. Fisher. The waves of advance of advantageous genes. Ann. Eugenics,7:353, 1937.

R. FitzHugh. Impulses and physiological states in theoretical models ofnerve membrane. Biophys. J., 1:445, 1961.

R. J. Field, E. Karas, and R. M. Noyes. Oscillations in chemical systems,Part 2. Thorough analysis of temporal oscillations in the bromate-cerium­malonic acid system. J. Am. Chern. Soc., 94:8649, 1972.

R. P. Feynman, R. B. Leighton, and M. Sands. The Feynman Lectures onPhysics. Addison-Wesley, Reading, MA, 1965.

R. J. Field and R. M. Noyes. Oscillations in chemical systems, IV. Limitcycle behavior in a model of a real chemical reaction. J. Chern. Phys.,60:1877, 1974.

E. Fermi, J. Pasta, and S. Ulam. Studies of nonlinear problems. In Col­lected Papers of E. Fermi, Vol. 2. University of Chicago Press, Chicago,1965.

352

[Fro92]

[Fun55]

[FW78]

[FW98]

[Gar70]

[Gar71a]

[Gar71b]

[Gau69]

[GC09]

[Gie81]

[GM72]

[GM79]

[GMP81]

[GMR07]

[GOC04]

[GP82]

[GPS02]

BIBLIOGRAPHY

J. Froyland. Introduction to Chaos and Coherence. CRC Press, New York,1992.

Y. C. Fung. An Introduction to the Theory of Aeroelasticity. John Wiley,New York, 1955.

H. I. Freedman and P. Waltman. Predator influence on the growth of apopulation with three genotypes. J. Math. BioI., 6:367, 1978.

C. Flynn and N. Wilson. A simple method for controlling chaos. Am. J.Phys., 66:730, 1998.

M. Gardner. Mathematical games. Sci. Am., 223 (10):120---0, 1970.

M. Gardner. Mathematical games. Sci. Am., 224 (2):112, 1971.

M. Gardner. Mathematical games. Sci. Am., 224 (4):117,1971.

G. F. Gause. The Struggle for Existence. Hafner, New York, 1969.

J. E. Goff and M. J. Carre. Trajectory analysis of a soccer ball. Am. J.Phys., 77:1020, 2009.

A. Gierer. Generation of biological patterns and form: Some physical,mathematical, and logical aspects. Progr. Biophys. molec. Biol., 37:1,1981.

A. Gierer and H. Meinhardt. A theory of biological pattern formation.Kybernetik, 12:30, 1972.

L. Glass and M. C. Mackey. Pathological conditions resulting from insta­bilities in physiological control systems. Ann. N. Y. Acad. Sci., 316:214,1979.

M. Giglio, S. Musazzi, and V. Perini. Transition to chaotic behavior viaa reproducible sequence of period-doubling bifurcations. Phys. Rev. Lett.,47:243, 1981.

G. Gandhi, B. Muthuswamy, and T. Roska. Chua's circuit for high schoolstudents. Int. J. Bifurcation Chaos, page 12, 2007.

G. A. Glatzmaier, D. E. Ogden, and T. L. Clune. Modeling the earth'sdyanamo. In R. S. J. Sparks and C. J. Hawkesworth, editors, State of thePlanet: Frontiers and Challenges in Geophysics. IUGG, 2004.

L. Glass and R. Perez. Fine structure of phase locking. Phys. Rev. Lett.,48:1772, 1982.

H. Goldstein, C. Poole, and J. Safco. Classical Mechanics, 3rd edition.Addison Wesley, New York, 2002.

BIBLIOGRAPHY 353

[GR65] I. S. Gradshteyn and I. M. Ryzhik. Tables of Integrals, Series, and Prod­ucts. Academic Press, New York, 1965.

[GR95a] G. A. Glatzmaier and P. H. Roberts. A three-dimensional convective dy­namo solution with rotating and finitely conducting inner core and mantle.Phys. Earth Planet. Int., 91:63, 1995.

[GR95b] G. A. Glatzmaier and P. H. Roberts. A three-dimensional self-consistentcomputer simulation of a geomagnetic field reversal. Nature, 377:203, 1995.

[GR96] G. A. Glatzmaier and P. H. Roberts. An anelastic evolutionary geodynamosimulation driven by compositional and thermal convection. Physica D,97:81, 1996.

[Gri99] D. Griffiths. Introduction to Electrodynamics, 3rd edition. Prentice Hall,Upper Saddle River, NJ, 1999.

[GSB86] L. Glass, A. Schrier, and J. Belair. Chaotic cardiac rhythms. In A. V.Holden, editor, Chaos. Princeton University Press, Princeton, 1986.

[GSB+04] P. Grim, E. Selinger, W. Braynen, R. Rosenberger, R. Au, N. Louie, andJ. Connolly. Reducing prejudice: A spatialized game-theoretic model forthe contact hypothesis. In J. Pollack, M. Bedau, P. Husbands, T. Ikegami,and R. A. Watson, editors, Artificial Life IX: Proceedings of the NinthInternational Conference on Artificial Life. MIT Press, Cambridge, 2004.

[GT96] H. Gould and J. Tobochnik. An Introduction to Computer SimulationMethods. Addison-Wesley, Reading, MA, 1996.

[GW64] C. M. Guldberg and P. Waage. Studies concerning affinity. C. M. Forhan­dlinger: Videnskabs-Selskabet i Christiana, page 35, 1864.

[GW79] C. M. Guldberg and P. Waage. Concerning chemical affinity. Erdmann'sJ. Pract. Chem., 127:69, 1879.

[GWDS95] A. Garfinkel, J. N. Weiss, W. L. Ditto, and M. L. Spano. Chaos controlof cardiac arrhythmias. Trends Cardiovasc. Med., 5:2, 1995.

[HA87] H. W. Hethcote and J. W. Van Ark. Epidemiological models for het­erogeneous populations: proportionate mixing, parameter estimation andimmunization programs. Math. Biosci., 84:85, 1987.

[Has75] M. P. Hassell. Density dependence in single-species populations. J. Anim.Ecol., 44:283, 1975.

[Has90] A. Hasegawa. Optical Solitons in Fibers. Springer-Verlag, New York, 2ndedition, 1990.

[Hat21] A. S. Hathaway. Pursuit in a circle. Am. Math. Monthly, 27:93, 1921.

354

[HDAB06]

[HeI95]

[Hen76]

[Het83]

[Het89]

[HetOO]

[HH64]

[HNKC09]

[HoI59a]

[HoI59b]

[HoI79]

[HoI04]

[Hop50]

[HT73]

[Inc64]

[Ing73]

BIBLIOGRAPHY

R. Hristovski, K. Davids, D. Araujo, and C. Button. How boxers decideto punch a target: Emergent behavior in nonlinear dynamical movementsystems. J. Sports Sci. Med., Combat Sports Special Issue:60, 2006.

H. Helmholtz. Sensation of Tone. Longmans Green, London, 1895.

M. Henon. A two-dimensional mapping with a strange attractor. Commun.Math. Phys., 50:69, 1976.

H. W. Hethcote. Measles and rubella in the United States. Am. J. Epi­demiol., 117:2, 1983.

H. W. Hethcote. Three basic epidemiological models. In S. A. Levin, T. G.Hallam, and L. J. Gross, editors, Applied Mathematical Ecology. Springer,New York, 1989.

H. W. Hethcote. The mathematics of infectious diseases. SIAM Rev.,42:599, 2000.

M. Henon and C. Heiles. The applicability of the third integral of motion:some numerical experiments. Astrophys. J., 69:73, 1964.

Derke R. Hughes, Albert H. Nuttall, Richard A. Katz, and G. CliffordCarter. Nonlinear acoustics in cicada mating calls enhance sound propa­gation. J. Acoust. Soc. Amer., 125:958, 2009.

C. Holling. The components of predation as revealed by a study of smallmammal predation of the European pine sawfly. Can. Entomol., 91:293,1959.

C. Holling. Some characteristics of simple types of predation and para­sitism. Can. Entomol., 91:385, 1959.

P. Holmes. A nonlinear oscillator with a strange attractor. Phil. Trans.Roy. Soc. London A, 292:419, 1979.

J. R. Holton. An Introduction to Dynamic Meteorology. Academic Press,New York, 3rd edition, 2004.

E. Hopf. The partial differential equation Ut + U U x , == U x x . Commun. PureAppl. Math., 3:201, 1950.

A. Hasegawa and F. D. Tappert. Transmission of stationary nonlinearoptical pulses in dispersive dielectric fibers. 1. Anomalous dispersion. Appl.Phys. Lett., 23:142, 1973.

E. L. Ince. Ordinary Differential Equations. Dover, New York, 1964.

A. P. Ingersoll. Jupiter's Great Red Spot: A free atmospheric vortex.Science, 182:1346, 1973.

BIBLIOGRAPHY 355

[IR90] E. Infeld and G. Rowlands. Nonlinear Waves, Solitons and Chaos. Cam­bridge University Press, Cambridge, 1990.

[Jac75] J. D. Jackson. Classical Electrodynamics, 2nd edition. John Wiley, NewYork, 1975.

[Jac90] E. A. Jackson. Perspectives of Nonlinear Dynamics. Cambridge UniversityPress, Cambridge, 1990.

[Jai97] N. K. Jaiswal. Military Operations Research. Kluwer Academic, New York,1997.

[JCOl] G. S. Jackson and J. Collinge. The molecular pathology of CJD: old andnew variants. J. Clin. Pathol., 54:393, 2001.

[JLH95] C. A. Jones, A. Longbottom, and R. Hollerbach. A self-consistent convec­tion driven geodynamo model, using a mean field approximation. Phys.Earth Planet Int., 92:119, 1995.

[JLSM64] R. C. Jaklevic, J. Lambe, A. H. Silver, and J. E. Mercereau. Quantuminterference effects in Josephson tunneling. Phys. Rev. Lett., 12:159, 1964.

[JonOO] A. J. Jones. Game Theory: Mathematical Models of Conflict. HorwoodPublishing, Chichester, U. K., 2000.

[Jos62] B. D. Josephson. Possible new effects in superconductive tunneling. Phys.Lett., 1:251, 1962.

[JS75] P. C. Jain and V. Srinivasan. A review of self-excited vibrations in oil filmjournal bearings. Wear, 31:219, 1975.

[Kar99] P. Kareiva. Coevolutionary arms races: Is victory possible? Proc. Natl.Acad. Sci. USA, 96:8, 1999.

[Kar03] V. P. J. Karmeshu. Nonlinear models of social systems. Economic andPolitical Weekly, 38:No.35, 2003.

[Kau76] D. J. Kaup. The three-wave interaction: A nondispersive phenomenon.Stud. Appl. Math., 55:9, 1976.

[Kau02] S. Kauffman. Ecology, the Ascendant Perspective. Oxford University Press,New York, 2002.

[KE96] L. D. Kiel and E. Elliot. Chaos Theory in the Social Sciences. Universityof Michigan Press, Ann Arbor, 1996.

[Ker04] B. Kerner. The Physics of Traffic. Springer, New York, 2004.

[KF70] B. E. Keen and W. H. W. Fletcher. Suppression of a plasma instability bythe method of asynchronous quenching. Phys. Rev. Lett., 24:130, 1970.

356

[KG95]

[KM27]

[KP70]

[KRB79]

[Kru91]

[KSW+95]

[KT99]

[Lai64]

[Lam64]

[Lan70]

[Lan16]

[Lan56]

[Lan64]

[Las69]

[Lau86]

[Lau97]

BIBLIOGRAPHY

D. Kaplan and L. Glass. Understanding Nonlinear Dynamics. Springer­Verlag, New York, 1995.

W. O. Kermack and A. G. McKendrick. Contributions to the mathematicaltheory of epidemics-I. Proc. R. Soc., 115A:700, 1927.

B. B. Kadomtsev and V. I. Petviashvili. On the stability of solitary wavesin weakly dispersive media. Sov. Phys. Dokl., 15:539, 1970.

D. J. Kaup, A. Rieman, and A. Bers. Space-time evolution of nonlinearthree-wave interactions. Rev. Mod. Phys., 51:275, 1979.

J. A. Krumhansl. Unity in the science of physics. Phys. Today, 44, No.3:33,1991.

A. Kageyama, T. Sato, K. Watanabe, R. Horiuchi, and T. Hayashi. Com­puter simulation of a magnetohydrodynamic dyanamo II. Phys. Plasmas,2:1421, 1995.

J. Kozlowski and A. T. Teriokhin. Allocation of energy between growthand reproduction: The pontryagin maximum principle solution for thecase of age- and season-dependent mortality. Evolutionary Ecology Res.,1:423, 1999.

A. K. Laird. Dynamics of tumor growth. Brit. J. Cancer, 18:490, 1964.

W. E. Lamb. Theory of an optical maser. Phys. Rev. A, 34:1429, 1964.

J. H. Lane. On the theoretical temperature of the sun under the hypoth­esis of a gaseous mass maintaining its volume by its internal heat anddepending on the laws of gases known to terrestrial experiment. Am. J.Sci. and Arts, 50:57, 1870.

F. W. Lanchester. Aircraft in Warfare: The Dawn of the Fourth Arm.Constable and Co., London, 1916.

F. W. Lanchester. Mathematics in warfare. In J. R. Newman, editor, TheWorld of Mathematics, Vol. 4. Simon and Schuster, New York, 1956.

W. L. Langer. The black death. Sci. Am., 210:114, 1964.

H. Lashinsky. Periodic pulling and the transition to turbulence in a sys­tem with discrete modes. In John Fox, editor, Turbulence of Fluids andPlasmas. Wiley, New York, 1969.

H. A. Lauwerier. One-dimensional iterative maps. In A. V. Holden, editor,Chaos. Princeton University Press, Princeton, 1986.

M. Laurent. Autocatalytic processes in cooperative mechanisms of priondiseases. FEBS Lett., 407:1, 1997.

BIBLIOGRAPHY 357

[LB34]

[Lin74]

[Lin76]

[Lin81]

[LJ24]

[LJH78]

[LLF82]

[LLP05]

[LM67]

[Lor63]

[Lor84]

[Lot56]

[LP80]

[LP90]

[LSW77]

[LY73]

H. Lineweaver and D. Burk. The determination of enzyme dissociationconstants. J. Am. Chem. Soc., 56:658, 1934.

D. A. Linkens. Analytic solutions of large numbers of mutually couplednearly sinusoidal oscillators. IEEE Trans. Circuit Syst., 21:294, 1974.

D. A. Linkens. Stability of entrainment conditions for particular formof mutually coupled van der Pol oscillators. IEEE Trans. Circuit Syst.,23:113, 1976.

P. Linsay. Period doubling and chaotic behavior in a driven anharmonicoscillator. Phys. Rev. Lett., 47:1349, 1981.

J. E. Lennard-Jones. On the determination of molecular fields. Proc. R.Soc. Lond. A, 106:463, 1924.

D. Ludwig, D. D. Jones, and C. S. Holling. Qualitative analysis of insectoutbreak systems: the spruce budworm and forest. J. Anim. Ecol., 47:315,1978.

A. Libchaber, C. Laroche, and S. Fauve. Period doubling cascade in Mer­cury, a quantitative measurement. J. Phys. Lett., 43:L211, 1982.

S. Lepri, R. Livi, and A. Politi. Studies of thermal conductivity in Fermi­Pasta-Ulam-like lattices. Chaos, 15:118, 2005.

E. B. Lee and L. Markus. Foundations of Optimal Control Theory. JohnWiley and Sons, New York, 1967.

E. N. Lorenz. Deterministic nonperiodic flow. J. Atmos. Sci., 20:130, 1963.

E. N. Lorenz. The local structure of a chaotic attractor in four dimensions.Physica D, 13:90, 1984.

A. J. Lotka. Elements of Mathematical Biology. Dover reprint, New York,1956.

E. W. Larsen and G. C. Pomraning. Asymptotic analysis of nonlinearmarshak waves. SIAM J. Appl. Math., 39:201, 1980.

R. Lima and M. Pettini. Suppression of chaos by resonant parametricperturbations. Phys. Rev. A, 41:726, 1990.

J. Lewis, J. M. W. Slack, and L. Wolpert. Thresholds in development. J.Theor. Biol., 65:579, 1977.

w. A. London and J. A. Yorke. Recurrent outbreaks of measles, chicken­pox, and mumps. I. Am. J. Epidemiol., 98:453, 1973.

358

[Lyn99]

[LynOl]

[Lyn06]

[MA87]

[MA89]

[May75]

[May76]

[May80]

[MC03]

[MehOO]

[Meh85]

[Men98]

[MG77]

[MIN04]

[Mit77]

BIBLIOGRAPHY

P. Lynch. The life cycles of extratopical cyclones. In M. A. Shapiro andS. Gronas, editors, Richardson's Marvellous Forecast. American Meteoro­logical Society, Boston, 1999.

P. Lynch. Weather forecasting: from woolly art to solid science. In R. P.Pearce, editor, Meteorology at the Millenium. Academic Press, San Diego,2001.

P. Lynch. The Emergence of Numerical Weather Prediction. CambridgeUniversity Press, Cambridge, 2006.

R. M. May and R. M. Anderson. Transmission dynamics of HIV infection.Nature, 236:137, 1987.

R. M. May and R. M. Anderson. The transmission dynamics of humanimmunodeficiency virus (HIV). In S. A. Levin, T. G. Hallam, and L. J.Gross, editors, Applied Mathematical Ecology. Springer, New York, 1989.

R. May. Stability and Complexity in Model Ecosystems, 2nd edition.Princeton University Press, Princeton, 1975.

R. M. May. Simple mathematical models with very complicated dynamics.Nature, 261:459, 1976.

R. M. May. Nonlinear phenomena in ecology and epidemiology. Ann. N. Y.Acad. Sci., 357:267, 1980.

T. Markvart and L. Castaner. Practical Handbook of Voltaics. Elsevier,New York, 2003.

W. R. Mebane. Congressional campaign contributions, district service,and electoral outcomes in the United States: Statistical tests of a formalgame model with nonlinear dynamics. In D. Richards, editor, PoliticalComplexity: Nonlinear Models of Politics. University of Michigan Press,Ann Arbor, 2000.

R. D. Mehta. Aerodynamics of sports balls. Annu. Rev. Fluid Mech.,17:151, 1985.

V. Mendez. Epidemic models with an infected-infectious period. Phys.Rev. E, 57:3622, 1998.

M. C. Mackey and L. Glass. Oscillations and chaos in physiological controlsystems. Science, 197:287, 1977.

F. Michor, Y. Iwasa, and M. A. Nowak. Dynamics of cancer progression.Nature Rev. Cancer, 4:197, 2004.

J. M. Mitchison. Cell cycle control models. In B. Drewinko and R. M.Humphrey, editors, Growth Kinetics and Biochemical Regulation of Nor­mal and Malignant Cells. Williams and Wilkins, Baltimore, 1977.

BIBLIOGRAPHY 359

[MK87]

[MM13]

[MMB90]

[MP94]

[MPD+07]

[MSG80]

[MSS73]

[MT95]

[Mue78]

[Mur76]

[Mur88]

[Mur02]

[Mur03]

[Mus37]

H. Meinhardt and M. Klingler. A model for pattern formation on the shellsof molluscs. J. Theor. Biol., 126:63, 1987.

L. Michaelis and M. I. Menten. Die kinetik der invertinwirkung. Biochem.Z., 49:333, 1913.

V. Mahajan, E. Muller, and F. M. Bass. New product diffusion modelsin marketing: A review and directions for research. J. of Marketing, 54:1,1990.

L. F. Mollenauer, M. J. Neubelt, S. G. Evangelides, J. P. Gordon, J. R.Simpson, and L. G. Cohen. Experimental study of soliton transmissionover more than 10,000 km in dispersion-shifted fibers. Opt. Lett., 15:1203,1988.

A. B. Murray and C. Paola. A cellular model of braided rivers. Nature,371:54, 1994.

N. Moll, E. Pascal, D. Dinh, J. Pillot, B. Bennetau, D. Rebiere, D. Moynet,Y. Mas, D. Mossayayib, J. Pistre, and C. Dejous. A Love wave immunosen­sor for whole E. coli bacteria detection using an innovative two-step im­mobilisation approach. Biosens. Bioelectron., 22:2145, 2007.

L. F. Mollenauer, R. M. Stolen, and J. P. Gordon. Experimental obser­vation of picosecond pulse narrowing and solitons in optical fibers. Phys.Rev. Lett., 45:1095, 1980.

N. Metropolis, M. L. Stein, and P. R. Stein. On finite limit sets for trans­formations on the unit interval. J. Combin. Theor., 15:25, 1973.

J. B. Marion and S. T. Thornton. Classical Dynamics of Particles andSystems. Saunders College Publishing, Orlando, 1995.

T. J. Mueller. Smoke Visualization of Subsonic and Supersonic Flow (TheLegacy of F. N. M. Brown). National Technical Information Service, U.S.Dept. of Commerce, Springfield, VA, 1978.

J. D. Murray. On travelling wave solutions in a model for the Belousov­Zhabotinsky reaction. J. Theor. Biol., 52:329, 1976.

J. D. Murray. How the leopard gets its spots. Sci. Am., March:80, 1988.

J. D. Murray. Mathematical Biology, 2nd edition. Springer-Verlag, Berlin,2002.

J. D. Murray. Mathematical Biology: I. An Introduction, 3rd edition.Springer-Verlag, Berlin, 2003.

M. Muskat. The Flow of Homogeneous Fluids Through Porous Media.McGraw Hill, New York, 1937.

360 BIBLIOGRAPHY

[MW004] N. Mantzaris, S. Webb, and H. G. Othmer. Mathematical modeling oftumor-induced angiogenesis. J. Math. Biol., 95:111, 2004.

[NAY62] J. S. Nagumo, S. Arimoto, and S. Yoshizawa. An active pulse transmissionline simulating nerve axon. Proc. IRE, 50:2061, 1962.

[NB95] A. H. Nayfeh and B. Balachandran. Applied Nonlinear Dynamics. Wiley,New York, 1995.

[NC74] T. Nagylaki and J. F. Crow. Continuous selection models. J. Theor. Populosi«; 5:267, 1974.

[New80] C. M. Newton. Biomathematics in oncology: modelling of cellular systems.Annu. Rev. Biophys. Bioeng., 9:541, 1980.

[Nic57] A. J. Nicholson. The self adjustment of populations to change. Cold SpringHarbor Symp. Quant. Biol., 22:153, 1957.

[NK86a] A. H. Nayfeh and A. A. Khdeir. Nonlinear rolling of biased ships in regularbeam seas. Int. J. Ship bldg. Prog., 33:84, 1986.

[NK86b] A. H. Nayfeh and A. A. Khdeir. Nonlinear rolling of ships in regular beamseas. Int. J. Ship bldg. Prog., 33:40, 1986.

[NM79] A. H. Nayfeh and D. T. Mook. Nonlinear Oscillations. Wiley, New York,1979.

[Nob74] J. V. Noble. Geographic and temporal development of plagues. Nature,250:726, 1974.

[NW69] A. C. Newell and J. A. Whitehead. Finite bandwidth, finite amplitudeconvection. J. Fluid Mech., 38:279, 1969.

[Ode80] G. M. Odell. Qualitative theory of systems of ordinary differential equa­tions, including phase plane analysis and the use of the Hopf bifurcationtheorem. In L. A. Segel, editor, Mathematical Models in Molecular andCell Biology. Cambridge University Press, Cambridge, 1980.

[OGY90] E. Ott, C. Grebogi, and J. A. Yorke. Controlling chaos. Phys. Rev. Lett.,64:1196, 1990.

[OIK005] Y. Ono, A. Ishiyama, N. Kasai, and A. Odawara. Development of micebiomagnetic measurement system using DC-SQUID magnetometer. IEEETrans. Appl. Supercond., 15:640, 2005.

[01s83] L. F. Olsen. An enzyme reaction with a strange attractor. Phys. Lett. A,94:454, 1983.

[PA05] N. J. R. Plowes and E. S. Adams. An empirical test of Lanchester's squarelaw: mortality during battles of the fire ant Solenopsis invicta. Proc. Ry.Soc. B, 272:1809, 2005.

BIBLIOGRAPHY 361

[Pal05a]

[Pal05b]

[PBGM86]

[PC89]

[PFTV89]

[PL68]

[PLA92]

[PRK68]

[Pro95]

[PST86]

[PT69]

[R76]

[Ras07]

[Ray83]

[RCM07]

[Ree95]

[Rey83]

G. Palmer. Physics for Game Players. Apress, New York, 2005.

T. Palmer. Global warming in a nonlinear climate-can we be sure? Eu­rophysics News, MarchiApril:42, 2005.

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mis­chenko. The Mathematical Theory of Opitmal Processes. Gordon andBreach, New York, 1986.

T. S. Parker and L. O. Chua. Practical Numerical Algorithms for ChaoticSystems. Springer-Verlag, Berlin, 1989.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Nu­merical Recipes. Cambridge University Press, Cambridge, 1989.

I. Prigogine and R. Lefever. Symmetry breaking instabilities in dissipativesystems, II. J. Chem. Phys., 48:1695, 1968.

M. Peastrel, R. Lynch, and A. Armenti. Terminal velocity of shuttlecockin vertical fall. In A. Armenti, editor, The Physics of Sports. AmericanInstitute of Physics, New York, 1992.

D. Pohl, I. Reinhold, and W. Kaiser. Experimental observation of stimu­lated thermal Brillouin scattering. Phys. Rev. Lett., 20:1141, 1968.

R. W. Prouty. Helicopter Performance, Stability, and Control. Krieger,Malablar, FL, 1995.

J. K. Park, K. Steglitz, and W. D. Thurston. Soliton-like behavior inautomata. Physica D, 19:423, 1986.

J. J. Pella and P. K. Tomlinson. A generalized stock production model.Bull. Inter-Am. Trop. Tuna Comm., 13:419, 1969.

O. E. Rossler. An equation for continuous chaos. Phys. Leti., 57A:397,1976.

E. Rasmusen. Games and Information: An Introduction to Game Theory,4th ed. Blackwell, Malden, MA, 2007.

Lord Rayleigh. On maintained vibrations. Philos. Mag., 15:229, 1883.

T. Roose, S. J. Chapman, and P. K. Maini. Mathematical models ofavascular tumor growth. SIAM Rev., 49:179, 2007.

G. Rees. The physics of medieval archery. Physics Rev., January, 1995.

O. Reynolds. An experimental investigation of the circumstances whichdetermine whether the motion of water shall be direct or sinuous, and ofthe law of resistance in parallel channels. Philos. Trans. R. Soc., page 935,1883.

362

[RGOO]

[Ric58]

[Ric95]

[RicOOa]

[RicOOb]

[Rob79]

[Rus44]

[Sap84]

[Sap99]

[Sch67]

[Sch79]

[Sch89]

[SCM73]

[Sco70]

[Sco81]

[Sco95]

BIBLIOGRAPHY

P. H. Roberts and G. A. Glatzmaier. Geodynamo theory and simulations.Rev. Mod. Phys., 72:1081, 2000.

W. E. Ricker. Handbook of Computations for Biological Statistics of FishPopulations. Fisheries Research Board of Canada, 1958.

L. F. Richardson. Weather Prediction by Numerical Process. CambridgeUniversity Press, Cambridge, 1922. Reprinted by Dover Publications,1995.

D. Richards. Nonlinear dynamics in games: convergence and stability ininternational environmental agreements. In D. Richards, editor, PoliticalComplexity: Nonlinear Models of Politics. University of Michigan Press,Ann Arbor, 2000.

D. Richards, editor. Political Complexity: Nonlinear Models of Politics.University of Michigan Press, Ann Arbor, 2000.

K. A. Robbins. Periodic solutions and bifurcation structure at high R inthe Lorenz model. J. Appl. Math., 36:457, 1979.

J. S. Russell. Report on waves. Rep. 14th, Brit. Assoc. Adv. Sci., 1844.

A. M. Saperstein. Chaos-a model for the outbreak of war. Nature,309:303, 1984.

A. M. Saperstein. Dynamical Modeling of the Onset of War. World Sci­entific, Singapore, 1999.

M. B. Schaffer. Lanchester models of guerilla engagements. The RANDCorporation, Santa Monica, CA, RM-5053-ARPA, DTIC No. AD648863,1967.

J. Schnakenberg. Simple chemical reaction systems with limit cycle be­havior. J. Theor. Biol., 81:389, 1979.

H. G. Schuster. Deterministic Chaos. VCH, Weinheim, Germany, 1989.

A. C. Scott, F. Y. F. Chu, and D. W. McLaughlin. The soliton: A newconcept in applied science. Proc. IEEE, 61:1443, 1973.

A. C. Scott. Active and Nonlinear Wave Propagation in Electronics. Wiley­Interscience, New York, 1970.

A. C. Scott. Introduction to nonlinear waves. In R. H. Enns, B. L.Jones, R. M. Miura, and S. S. Rangnekar, editors, Nonlinear Phenom­ena in Physics and Biology. Plenum, New York, 1981.

S. K. Scott. Oscillations, Waves and Chaos in Chemical Kinetics. OxfordUniversity Press, New York, 1995.

BIBLIOGRAPHY 363

[Seg69]

[SeI68]

[Shi80]

[SHL70]

[Si190]

[SJD+94]

[SM96]

[SMK89]

[Spa82]

[SR96]

[SSM81]

[Ste88]

[Str94]

[Sut88]

[SW58]

[Tet83]

[Tho05]

L. A. Segel. Distant sidewalls cause slow amplitude modulation of cellularconvection. J. Fluid Mech., 38:203, 1969.

E. E. Sel'kov. Self-oscillations in glycolysis. Eur. J. Biochem., 4:79, 1968.

N. Shigesada. Spatial distribution of dispersing animals. J. Math. Biol.,9:85, 1980.

L. Simpson-Herren and H. H. Lloyd. Kinetic parameters and growth curvesfor experimental tumor systems. Cancer Chemother. Rep. Part I, 54:143,1970.

Y. Silberberg. Collapse of optical pulses. Opt. Lett., 15:1282, 1990.

S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L.Ditto. Controlling chaos in the brain. Nature, 370:615, 1994.

A. Swift and E. Moroz. Wind turbines. In R. C. Dorf, editor, The Engi­neering Handbook. CRC Press, Boca Raton, FL, 1996.

A. M. Saperstein and G. Mayer-Kress. Chaos versus predictability informulating national strategic security policy. Am. J. Phys., 57:217, 1989.

C. Sparrow. Bifurcations in the Lorenz Equation. Springer-Verlag, Berlin,1982.

x. Song and P. Richards. Seismological evidence for differential rotationof the earth's inner core. Nature, 382:221, 1996.

M. B. Simson, J. F. Spear, and E. N. Moore. Stability of an experimen­tal atrioventricular reentrant tachycardia in dogs. Heart Circ. Physiol.,9:H947, 1981.

A. Stepanek. The aerodynamics of tennis balls-the topspin lob. Am. J.Phys., 56:138, 1988.

S. H. Strogatz. Nonlinear Dynamics and Chaos. Addison-Wesley, Reading,MA,1994.

R. M. Sutherland. Cell and environment interactions in tumor microre­gions. Nature Rev. Cancer, 4:177, 1988.

M. P. Shepard and F. C. Withler. Spawning stock size and resutant pro­duction for Skeena sockeye. J. Fish. Res. Board Can., 15:1007, 1958.

G. Tetzlaff. Albedo of the Sahara. Cologne Univ. Satellite Meas. of Radi­ation Budget Parameters, October:60, 1983.

A. J. Thorpe. Climate change prediction, a challenging scientific problem.Institute of Physics Report, 2005.

364 BIBLIOGRAPHY

[TK93a] Z. Toth and E. Kalnay. Ensemble forecasting at NMC: Operational im­plementation. Weather Forecasting, 8:379, 1993.

[TK93b] Z. Toth and E. Kalnay. Ensemble forecasting at NMC: The generation ofperturbations. Bull. Am. Meteoro. Soc., 74:2317, 1993.

[TM96] T. Tang and J. C. McConnell. Autocatalytic release of bromine from Arcticsnow pack during polar sunrise. Geophys. Res. Lett., 23:2633, 1996.

[Tod89] M. Toda. Theory of Nonlinear Lattices. Springer-Verlag, Berlin, 2nd edi­tion, 1989.

[Tor81] S. Torven, Modified Korteweg-De vries equation for propagating doublelayers in plasmas. Phys. Rev. Lett., 47:1053, 1981.

[Tor86] S. Torven. Weak double layers in a current carrying plasma. Phys. Scr.,33:262, 1986.

[TPJ82] J. S. Testa, J. Perez, and C. Jeffries. Evidence for universal chaotic be­havior of a driven nonlinear oscillator. Phys. Rev. Lett., 48:714, 1982.

[TPS98] C. Tomlin, G. J. Pappas, and S. Sastry. Conflict resolution for air trafficmanagement: a study in multi-agent hybrid systems. IEEE Transactionson Automatic Control, 43, April 1998.

[TTM+08] E. Tamaseviciute, A. Tamasevicius, G. Mykolaitis, S. Bumeliene, andE. Lindberg. Analogue electrical circuit for simulation of the Duffing­Holmes equation. Nonlinear Analysis: Modelling and Control, 13:241,2008.

[Tur52] A. M. Turing. The chemical basis of morphogenesis. Philos. Trans. Ry.Soc. London, B237:37, 1952.

[Tys76] J. J. Tyson. The Belousov-Zhabotinskii reaction. In Lecture Notes inBiomathematics, Vol. 10. Springer-Verlag, New York, 1976.

[Tys85] J. J. Tyson. A quantitative account of oscillations, bistability, and travelingwaves in the Belousov-Zhabotinsky reaction. In R. J. Field and M. Burger,editors, Oscillating and Traveling Waves in Chemical Systems. Wiley, NewYork, 1985.

[UJ09] R. Uhlaf and M. Janura. Pontragin's maximum principle and optimzationof the flight phase in ski jumping. Acta Univ. Palacki. Olomuc., Gymn,39:61, 2009.

[Ula62] S. M. Ulam, On some mathematical problems connected with patterns ofgrowth of figures. Proc. Symp. Appl. Math., 14:215, 1962.

[Ula97] R. Ulanowicz. Ecology, the Ascendant Perspective. Columbia UniversityPress, New York, 1997.

BIBLIOGRAPHY 365

[VD01] V. Vitagliano and G. D'Errico. A simple kinetic model to describe theprogression of prion disease. Phys. Chem. Chem. Phys., 3:4547, 2001.

[vdP26] B. van der Pol. On relaxation oscillations. Philos. Mag., 2:978, 1926.

[vdPvdM28] B. van der Pol and J. van der Mark. The heart beat considered as arelaxation oscillator and an electrical model of the heart. Philos. Mag.,6:763, 1928.

[Ver90] F. Verhulst. Nonlinear Differential Equations and Dynamical Systems.Springer-Verlag, Berlin, 1990.

[vNM44] J. von Neumann and O. Morgenstern. Theory of Games and EconomicBehavior. Princeton University Press, Princeton, 1944.

[Vog94] S. Vogel. Life in Moving Fluids. Princeton University Press, Princeton,1994.

[VoI26a] V. Volterra. Fluctuations in the abundance of a species considered math­ematically. Nature, 118:558, 1926.

[VoI26b] V. Volterra. Variazioni e fluttuazioni del numero d'individui in specieanimali conviventi. Mem. R. Accad. Naz dei Lincei, 2:31, 1926.

[Waa64] P. Waage. Experiments for determining the affinity law. C. M. Forhan­dlinger i Videnskabs-Selskabet i Christiana, page 92, 1864.

[WBB02] P. Waltman, J. Braselton, and L. Braselton. A mathematical model of abiological arms race with a dangerous prey. J. Theor. Biol., 218:55, 2002.

[WC69] C. H. Waddington and R. J. Cowe. Computer simulation of a mulluscanpigmentation pattern. J. Theor. Biol., 25:219, 1969.

[WHH+88] A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M.Kirsschner, and D. E. Experimental observation of the fundamental darksoliton in optical fibers. Phys. Rev. Lett., 61:2445, 1988.

[WLPL06] E. Wertheim, A. Love, C. Peck, and I. Littlefield. Skills for ResolvingConflict. Eruditions Publishing, Melbourne, Australia, 2006.

[WoI86] S. Wolfram, editor. Theory and Applications of Cellular Automata. WorldScientific, Singapore, 1986.

[WoI02] S. Wolfram. A New Kind of Science. Wolfram Media, Champaign, IL,2002.

[WoI06] J. Wolfers. Point shaving: Corruption in ncaa basketball. Amer. Econ.Rev., 96:279, 2006.

[WS81] T. A. Witten and L. M. Sander. Diffusion limited aggregration: A kineticcritical phenomenon. Phys. Rev. Lett., 47:1400, 1981.

366

[WS03]

[YK82]

[YL73]

[You92]

[ZB03]

[Zha91]

[ZK65]

[Zwi89]

[ZZ70]

[ZZ07]

BIBLIOGRAPHY

B. J. West and N. Scafetta. Nonlinear dynamical model of human gait.Phys. Rev. E, 67:051917, 2003.

w. J. Yeh and Y. H. Kao. Universal scaling and chaotic behavior of aJosephson junction analog. Phys. Rev. Lett., 49:1888, 1982.

J. A. Yorke and W. A. London. Recurrent outbreaks of measles, chicken­pox, and mumps. II. Am. J. Epidemiol., 98:469, 1973.

R. M. Youngson. Collins Dictionary of Medicine. Collins, UK, 1992.

A. R. Zangerl and M. R. Berenbaum. Phenotype matching in wild parsnipand parsnip webworms: causes and consequences. Evolution, 57:806, 2003.

A. M Zhabotinskii. A history of chemical oscillations and waves. Chaos,1:379, 1991.

N. J. Zabusky and M. D. Kruskal. Interaction of "solitons" in a collisionlessplasma and the recurrence of initial states. Phys. Rev. Lett., 15:240, 1965.

D. Zwillinger. Handbook of Differential Equations. Academic Press, NewYork, 1989.

A. N. Zaikin and A. M Zhabotinskii. Concentration wave propagationin two-dimensional liquid-phase self-organizing system. Nature, 225:535,1970.

K. Zimmermann and I. Zeidis. Worm-like locomotion as a problem ofnonlinear dynamics. J. Theor. Appl. Mech., 45:179, 2007.

Index

Accuweather, 245acetic acid, 257acetylcholine, 261Acta Eruditorum, 34action potential, 26activator-inhibitor mechanism, 272adiabatic equation of state, 63Afghanistan, 342aging affects gait, 192aim of text, 3aimed fire, 335air traffic management, 344aircraft wing, 139airfoil, 139

aspect ratio, 140downwash, 139edge effects, 139stall angle, 140thin, 139upside down, 186

airtrackglider, 149linear, 149

Alaways, LeRoy, 138albedo, 252

asphalt, 252bare soil, 252coniferous forest, 252deciduous forest, 252desert sand, 252fresh snow, 252green grass, 252new concrete, 252ocean ice, 252ocean surface, 252

algorithm

367

forward Euler, 12numerical stability, 117RK4, 16RKF45,20Runge-Kutta, 16sine-Gordon, 115variable step, 20Von Neumann criterion, 117Zabusky-Kruskal, 112

allele, 316Allen, Holless, 188Altman, Sidney, 278American Civil War, 311, 341Ames Research Center, 173Amundsen, Roald, 222Anderson-May model, 305Andromeda Strain, 10anelastic approximation, 225angiogenesis hypothesis, 301angle of attack, 139, 168anharmonic potential, 166annual plant propagation, 27anticyclonic, 239Antonine plague, 310apsides, 155arc discharge, 201arms expenditures, 324, 327arms race

bilateral, 327chaos, 332coevolutionary, 312devotion, 327escalating, 322model, 328multi-nation, 342Richardson model, 324

R. H. Enns, It’s a Nonlinear World, DOI 10.1007/978-0-387-75340-9,© Springer Science+Business Media, LLC 2011

368

runaway, 326tripolar model, 334Waltman-Braselton, 316

Armstrong, James, 281artificial neural network, 324aspect ratio, 139, 140aspirin, 257asymmetric warfare, 342atrioventricular conduction, 95attractor

Rossler, 67San Marco, 92strange, 54

attrition warfare, 341aurora, 233Aurora Australis, 218Aurora Borealis, 218autocatalysis, 255automata

one-dimensional, 119two-dimensional, 122

autonomous, 36avascular tumor growth, 301Axelrod, Robert, 343axial induction factor, 140

Backlund transformation, 104BAC Lightning, 140backspin, 138, 182bacteria, 275, 282badminton bird, 184badminton birdie, 138Bailey, Sean, 171balance wheel, 30baleen whales, 26, 65ballistic coefficient, 169Barnsley, Michael, 94barotropic fluid, 237barotropic vorticity equation, 237baseball, 138basic reproduction rate, 285basin of attraction, 44Bass diffusion model, 97Bass formula

modified, 98

INDEX

Bass, Fred, 97BATNA, 344battle of Agincourt, 187battle of Ardennes, 337battle of Britain, 343battle of Iwo Jima, 336beam seas, 170Bear Archery, 188Bearce, David, 324Beckerman, Linda, 339Beckham, David, 176Beijing Olympics, 164Belousov-Zhabotinskii reaction, 263Bendixson negative criterion, 51Bennett, Richard, 140Benton, Oregon, 313Bernoulli ODE, 61Bernoulli, Johann, 34Betz limit, 140Betz, Albert, 140bias current, 204bifurcation, 44, 72

Hopf,46pitchfork, 45, 73saddle-node, 44, 205transcritical, 45, 73

bifurcation diagram, 77biochemical switch, 26biomimetic control, 171Bjerknes, Vilhelm, 250black death, 292black spleenwort, 94blade element theory, 140blade flapping, 140Bloch wall, 104Bloch, Felix, 104blood cells, 14Boeing 747, 140, 164Boeing Company, 140bone marrow, 14Boston Red Sox, 178botulinum toxin, 313Bouguer, Pierre, 32Boven, Bradley, 343bovine spongiform, 296

INDEX

boxing, 192Boyd, John, 339brachistochrone, 34braided stream, 122brain, 324Braselton, James, 314Braselton, Lorraine, 314breather mode, 125British Met office, 246broaching, 170Brodie, Edmund, Jr., 312Brusselator, 266BSE, 296bubonic plague, 292budget cycle, 327Burgers's equation, 125Burgers, Johannes, 125butterfly attractor, 54

CAbraided stream, 122

Campbell, David, 152Canberra fire, 245cancer, 301

avascular stage, 301metastasis, 301necrotic center, 301

Cantor set, 57capacitor, 194capacity dimension, 56car racing, 186carbon dioxide, 250, 303cardiac death, 268Carlos, Robert, 176carrying capacity, 5, 339castrating fungi, 322cell

cancer, 301excited, 122normal, 301quiescent, 122refractory, 122

cellular automata, 119center of mass, 166Cessna 172, 140

Chandrasekhar, S., 24chaos, 27

control, 89period doubling, 77route to, 77

characteristic direction, 113SGE, 115

characteristic length, 132Charney, Jules, 236chemical oscillator, 263chemical reaction

autocatalytic, 255first-order, 298law of mass action, 255ozone depletion, 257reversible, 255third-order, 297zero-order, 298

chemical wave, 268chemostat, 65chemotaxis, 275Chesneau, Lee, 245Chiao, Raymond, 216chromosome, 316Chua's circuit, 197Chua, Leon, 197cicada nonlinearity, 28circle map, 96civil war

Sri Lankan, 342CJD, 296Clay mathematics prize, 215cobweb diagram, 74, 96coevolution, 313Cole, J. D., 125college basketball, 192competing armies, 339compound bow, 188computer algebra recipes, 20conductivity, 209Confederate army, 341conflict resolution model, 344conic section, 156contact number, 285control forecast, 246

369

370

control parameter, 44control problem, 68control variables, 68convective cell, 222Conway, John, 127Cooper pair, 203cooperation, 343cooperative phenomena, 273Coors Field, 191coral snake, 312core-mantle boundary, 222Coriolis acceleration, 237Coriolis force, 214, 224, 239Coriolis parameter, 237corruption, 192Coulomb's law, 209Courant stability condition, 124Crichton, Michael, 9crisis instability, 332critical current, 203CSS model, 304cubic map, 91cumulative oil production, 7Curie temperature, 222curling, 192curvature, 6curve of pursuit, 32curveball, 178cyanide, 313cyclic selection, 322, 323cyclonic, 239

D'Ancona, Humberto, 17damped pendulum

forced, 144dark soliton, 230Darwinian selection, 278de Vries, Gustav, 101Debye, Peter, 152defect, 343dekameter, 242Depressaria pastinacella, 322Devil's staircase, 96devotion, 327dielectric constant, 209

INDEX

difference approximationbackward, 110central, 110forward, 110

difference equation, 9atrioventricular conduction, 95Barnsley, 94circle map, 96cubic map, 91density-limited, 93finite approximation, 12fractal fern, 94fractal tree, 94Henon, 90hematopoiesis, 14linear, 9logistic, 10, 27Mandelbrot, 84nonlinear, 10Pella-Tomlinson, 23predator-prey, 92Ricker's sockeye, 94Saperstein arms race, 327sine map, 91spruce budworm, 12standard map, 97tent map, 95

differential equation3-wave, 229autocatalytic, 255badminton bird, 184barotropic vorticity, 237baseball, 180Bernoulli, 61, 215, 285blade flapping, 140brachistochrone, 34breather solution, 125Brusselator, 267Buckmaster, 108Burgers, 125chemotaxis, 275Chillingworth-Holmes, 226Chua circuit, 197circular pursuit, 62competing food supply, 65

INDEX

Courant stability condition, 124CSS model, 304damped pendulum, 143double pendulum, 166Duffing, 54, 153Duffing-Holmes, 232Euler-Lagrange, 34fish harvesting, 24Fisher, 125, 270FitzHugh-Nagumo, 26forced pendulum, 145fox rabies, 305fox rabies spread, 292generalized Lanchester, 338glycolysis, 274golf ball, 182Gompertz, 307Hamilton's, 162hard spring, 149Holling predator-prey, 314inverted Duffing, 54Josephson junction circuit, 205Kadomtsev-Petviashvili, 126KdV, 101KPI, 126KPII, 126Lagrange, 146, 219Lanchester linear, 335Lanchester nonlinear, 337linear, 4linear pursuit, 32logistic delay, 24Lorenz, 53Lot ka-Volterra, 17, 262Malthus, 9marble pendulum, 165Maxwell, 209method of characteristics, 115Michaelis-Menten, 260modified KdV, 123Navier-Stokes, 213nested limit cycle, 66nonlinear, 4nonlinear diffusion, 124nonlinear Schrodinger, 211

371

nonlinear spring, 63nonlinear superposition, 123numerical stability, 117orbital motion, 156Oregonator, 263predator-prey, 27prion disease, 298Rossler, 67reaction-diffusion, 269Riccati, 61Richardson arms race, 324saturable Volterra, 64Schnakenberg, 275SEIR, 306semistable limit cycle, 66simple harmonic, 141simple pendulum, 141sine-Gordon, 104SIR, 286SIS, 284spherical pendulum, 165stable limit cycle, 49stimulated thermal Brillouin, 216symbiosis, 23symbiotic interaction, 64Toda, 168tripolar arms race, 334unstable limit cycle, 50van der Pol, 201Verhulst, 10Von Neumann stability criterion, 117Waltman-Braselton, 316wing rock, 168Zabusky-Kruskal algorithm, 117

diffusion-limited aggregation, 127dimension

capacity, 56fractal, 54

dimensionless form, 5diode, 196disease

amebiasis, 283anthrax, 283brucellosis, 283cancer, 301

372

chickenpox, 283cholera, 283Creutzfeldt-Jakob, 296encephalitis, 283endemic, 284filariasis, 283gonorrhea, 283herpes, 283HIV (AIDS), 283mad cow, 296malaria, 283measles, 283meningitis, 283mumps, 283onchocerciasis, 283plague, 283pneumonia, 283poliomyelitis, 283rabies, 283rubella, 283sandfly fever, 283schistosomiasis, 283smallpox, 283strep throat, 283syphillis, 283tick fever, 283trichinosis, 283trypanosomiasis, 283tuberculosis, 283tularemia, 283typhoid fever, 283yellow fever, 283

disease growth, 296disease model

age-structured, 291SEIR, 306SIR (no vital dynamics), 286SIR (vital dynamics), 289SIS, 284

disease transmission, 282disk dynamo model, 226dispersion

anomalous, 211group velocity, 211normal, 213

INDEX

displacement vector, 209dissipative map, 92divorce prediction, 97doping, 199Douady's rabbit, 86Douady, Adrien, 86double reciprocal plot, 261double scroll attractor, 198, 199Douglass, David, 253Dow Jones average, 9downwash, 139drag coefficient, 137drag force, 131drag law

Newton's, 133Stokes's, 134

Dresher, Melvin, 343drinking bird, 203drug war, 343Duffing equation, 54Duffing-Holmes oscillator, 232

earcubic difference tone, 150

Earth's crust, 222eccentricity, 156E. coli, 9, 27economic sanctions, 323eddy viscosity, 237Eden growth model, 127Eden, Murray, 127Edwards, Sean, 342Eggers, Jens, 170Eigen, Manfred, 278Einstein, Albert, 156El Nino, 244electrical circuit

Chua, 197Josephson junction, 203negative resistance, 197nonlinear capacitor, 196nonlinear inductor, 193piecewise-linear, 197tunnel diode, 199

electrostrictive force, 214

INDEX

elliptic function, 31, 142elliptic integral

complete, 142emissivity, 252energy allocation, 69English longbow, 187ENIAC, 236ensemble forecasting, 246ensemble mean, 246ensemble spread, 246entrainment, 145environmental treaty, 323enzyme

acetylcholine esterase, 261carbonic anhydrase, 261catalase, 261fumerase, 261urease, 261

enzymes, 257epidemic, 281epidemic curve, 287epidermis, 272epileptic seizures, 307Erehwon, 17, 25error

round-off, 109truncation, 109

Esaki, Leo, 199, 203Escherichia coli, 10Euler algorithm, 12Euler strut, 150European Geophysical Union, 236European pine sawfly, 314European weather patterns, 253excitable medium, 122, 268exponential function, 5exports, 343

falling sand, 134Faraday constant, 303Faraday's law, 209, 223fastball, 180feedback coupled nonlinear oscillator, 171Feigenbaum number, 76Feigenbaum, Mitchell, 76

Ferdinand, Archduke Francis, 326Fermi, Enrico, 152ferroin, 263ferroin indicator, 263ferry naviagation, 69fiber spinning, 170Field, Richard, 264finite difference approximation, 12fire ant, 337fireflies, 145fish harvesting, 24Fisher solitary wave, 274Fisher's equation, 125, 270Fisher, Ronald, 270FitzHugh-Nagumo model, 26fixed point, 36

I-dimensional map, 712-dimensional map, 82atrioventricular conduction, 95classification, 38degenerate, 41delayed logistic map, 83focal, 38Henon map, 92higher order, 41logistic map, 71Mandelbrot map, 91nodal, 38nonlinear map, 71predator-prey map, 92saddle, 37, 102saddle-vortex, 41stability criterion, 73stable, 38topology, 41unstable, 38, 72vortex, 37, 38

Fjortoft, Ragnar, 236fleas, 292Flood, Merrill, 343flux conservation, 209flux quantum, 208focal point, 38forensic economics, 192forward Euler method, 12

373

374

four-wave mixing, 232Fourier transform, 59, 60FPU anomaly, 152fractal

dimension, 56non-self-similar, 67self-similar, 57

fractal fern, 94fractal tree, 94France, 327Frederick Lanchester

disk brakes, 335fuel injection, 335gas engine starter, 335operations research, 335rack-and-pinion steering, 335

free flight, 344free kick, 176free trade, 343Froyland, Jan, 158fuel efficiency, 137fumerate, 261fur catches, 19furanocoumarin, 322

bergapten, 322isopimpinellin, 322sphondin, 322xanthotoxin, 322

gain coefficient, 217Game of Life, 127game theory models, 323Gamma function, 166Gardner, Martin, 127garter snake, 312gastrointestinal tract, 201Gause, G. F., 5gene, 270, 316gene mutation, 301general relativity, 156genetic information, 278genotype, 316geodynamo, 222geodynamo model, 226geodynamo simulations, 231

INDEX

geographic mosaic theory, 323Geological Survey of Canada, 221geometric growth, 9geopotential function, 241geopotential height, 241geostrophic balance, 239geostrophic wind, 239Germany, 327Giaever, Ivar, 199, 203Gierer, Alfred, 277Gierer-Meinhardt model, 277Glass, Leon, 268Glatzmaier, Garry, 225global climate models, 253global forecast model, 245glucose, 257, 303glycolysis, 273GNP, 327gnus, 25, 42golf ball, 138golf ball trajectory, 182Gompertz model, 307GR model, 226gradient wind, 250Grant, Ulysses, 341gravitational constant, 156greenhouse gases, 250grid point, 37Grim, Patrick, 128ground effect car, 186group velocity, 211Guldberg, Cato, 255Gulf of Carpentaria, 128

Henon attractor, 90Henon-Heiles potential, 161Hadley cell, 251Hamilton's equations, 162Hamilton, William, 343Hamiltonian, 69Hamiltonian chaos, 161handling time, 314Hardy-Weinberg law, 316harvesting fish, 69Hasegawa, Akira, 210

INDEX

heart, 95heart attack, 269helicopter rotor, 140Helmholtz, Heinrich, 150helminth, 282hematopoiesis, 14hematopoiesis regulation, 14hemoglobin, 257, 273Henry V, 187herd immunity, 282, 291heritability, 322heron, 313Hethcote, Herbert, 282, 307HIV transmission and AIDS, 307hockey puck, 175

air drag, 191Holling equations, 314Holling predation

Type 1,314Type 11,314Type III, 314

Holling, C.S., 314holomorphic dynamics, 86Hooke's law, 30Hooke, Robert, 30Hopf, E., 125Hopf-Cole transformation, 125Hubbert curve, 7, 22Hubbert, M. King, 6Hudson's Bay Company, 19Hughes, Derke, 28human conflict, 323human gait, 171human motor control, 171Hummer, 137Huygens, Christian, 145hydrostatic balance, 241hypersurface, 162hysteresis loop, 48, 155

immune response, 289immunity

permanent, 286temporary, 286

incompressible fluid, 214

375

inductance coil, 193industrial nations, 343Indy car, 190infectives, 283Infeld, Eryk, 101inflection point, 6influenza, 281initial condition sensitivity, 55ink jet printing, 170Inland Taipan, 313inner core, 222

boundary, 222insect reproduction, 69insulating barrier, 204insurgencies, 344intermittency, 91international relations, 342intrinsic growth rate, 4inverse square law, 156ion acoustic wave, 101IPCC report (2007), 253Iraq, 342iris diaphragm, 30iron core inductor, 193isobar, 239Italy, 327iteration, 153

Jackson, E. Atlee, 119jai alai ball, 175Jaklevic, Robert, 208Johnson, Ian, 343Jones, Antonia, 323Josephson effect, 204, 228Josephson junction, 203

bistability, 207Josephson, Brian, 199journal bearings, 201Julia set, 85Julia, Gaston, 85jump phenomena, 155

Kadomtsev-Petviashvili equation, 126Kadtke, Jim, 342KAM torus, 164

376

Kareiva, Peter, 322Karmeshu, V. P. Jain, 28katabatic wind, 250Kauffman, Stuart, 257KdV equation, 101Kepler's third law, 159Kerr index, 210kinematic viscosity, 237kingfisher, 313kink-antikink collision, 117kink-kink collision, 126kite, 139Koch curve, 57Koch's snowflake, 67Korean Airlines, 326Korteweg, Diederik, 101Korzybski, Alfred, 71Krebs cycle, 302krill, 65Kruskal, Martin, 110kuru, 296

l'Hopital, Guillaume de, 34La Nina, 244Lagrangian, 146, 219Lambe, John, 208Lanchester equations, 335Lanchester linear law, 335Lanchester square law, 335Lanchester, Frederick, 335Lane-Emden equation, 63Laplace's equation, 215laughing sickness, 296Lauwerier model, 27Lefever, Rene, 266Leibniz, Gottfried, 34Lenhart, Suzanne, 342Lennard-Jones potential, 278leopard spots, 272Lepri, Stefano, 153Lester, John, 178Lidar, 312Lie group, 108lift coefficient

soccer ball, 191

tennis ball, 190lift force, 215light bullet, 213limit cycle, 49, 206

Brusselator, 266circular, 66nested, 66Oregonator, 265semistable, 66stable, 49unstable, 50

linear pursuit, 32linear superposition, 31linear warfare equations, 335Lineweaver-Burk plot, 261liquid drop formation, 171little ice age, 253Lockwood, Mike, 253locus, 316logistic curve, 5, 309logistic difference equation, 10logistic map, 71Lorentz force, 220Lorenz model, 53Lorenz, Edward, 53Los Alamos, 226Lotka, Alfred, 16Lotka-Volterra mechanism, 261Lotka-Volterra ODEs, 17Lucilia cuprina, 24Lyapunov exponent, 80

logistic map, 81Lyapunov, Aleksandr, 80Lynch, Peter, 236

Mendez, Vicene, 296MacKay, Niall, 343magnetic decay, 224magnetic dipole, 218magnetic field

decay, 224drift, 226flip, 226

magnetic flux, 193magnetic saturation, 193

INDEX

INDEX

magnetization, 209magnetocardiography, 208magnetoencephalography, 208magnetohydrodynamics, 223Magnus force, 138, 178Magnus, Heinrich, 138malate, 261Malthus ODE, 4Malthus, Thomas, 4Malthusian population growth, 4Mandelbrot map, 84Mandelbrot set, 84Mandelbrot, Benoit, 84Maniac I, 152mantle, 222map

kth-iterate, 71circle, 96classifying fixed points, 83cubic, 91delayed logistic, 82dissipative, 92first-order, 71fixed points, 71logistic, 71Mandelbrot, 84nonlinear, 71one-dimensional, 71predator-prey, 92second-iterate, 75sine, 91standard, 97, 167tent, 95third-iterate, 91two-dimensional, 82unimodal, 77

Maple, 20marital interaction, 97marketing, 98marriage repair, 97Mars probe, 69Mathcad, 20Mathematica, 20Maunder minimum, 253maximum range, 187

Maxwell-Ampere law, 209May, Robert, 3Mebane, Walter, Jr., 323Mehta, Rabi, 173Meinhardt, Hans, 277melanin, 272Mercereau, James, 208Mercury

precession of, 155mesh point, 111meter stick

period, 166methane, 250method of characteristics, 113Metropolis, N., 95MHD geodynamo model, 225Michaelis constant, 259Michaelis-Menten equation, 260Michaelis-Menten kinetics, 257Milankovic, Milutin, 253Milankovitch cycle, 253Mill, John Stuart, 311millibar, 240Mimas, 159modified KdV equation, 123Monarch butterfly, 312Morens, David, 309Morgenstern, Oscar, 323Morning Glory cloud, 128Murray, A. B., 122Murray, Jim, 272, 273, 276, 292mutations, 278myxoma virus, 23myxomatosis, 23

nanosecond pulse, 209Napoleon, 256NASA, 140Nathan, Alan, 180national census, 9natural logarithm, 4natural selection, 313Navier, Claude-Louis, 213Navier-Stokes equations, 213NCEP, 244, 251

377

378

NCEP global model, 246negative resistance, 197, 199neon lamp, 232Nernst-Einstein equation, 303nerve cell firing, 26nervous system, 324neurlli network, 307, 323neuron firing, 307neurons, 324neurotoxin, 313Newell-Whitehead-Segel equation, 271Newitt, Larry, 222newt, 312Newtonian fluid, 214nitrous oxide, 250NLSE, 211NOAA climate model, 253Nobel chemistry prize, 278nodal point, 38noise vs. chaos, 86non-A hepatitis, 288non-B hepatitis, 288non-Newtonian fluid, 214nonautonomous, 36nonautonomous ODE, 54noninteger dimension, 54nonlinear acoustics, 28nonlinear capacitance, 196nonlinear drag, 131nonlinear force law, 30nonlinear game theory, 323nonlinear inductance, 193nonlinear lift, 138nonlinear map, 71nonlinear optics, 209nonlinear resonance, 155nonlinear social systems, 28nonlinear spring, 63nonlinear superposition, 63, 123normal modes, 152North Atlantic Oscillation index, 251North Magnetic Pole, 218

drifting, 222northern Australia, 128northern lights, 218

Noyes, Robert, 264nucleotide sequence, 278numerical cells, 119numerical instability, 20numerical mesh, 111numerical simulation, 109numerical solution, 12numerical stability, 117nutrient, 275

ocean ridge, 222ocean trench, 222Oceanic Nino Index, 244ODE system, 12Ohm's law, 209oil fields, 8okta, 251Old Faithful, 203Olympic peninsula, 313Oncorhynchus nerka, 93OODA loop, 339op amp, 197OPEC, 8optical fiber, 210optical soliton, 211optimal control variables, 68optimization, 68ordinary point, 36Oregon coast, 127Oregonator, 263oscillator

chaotic, 61Duffing, 55

Osler, William, 281outbreak of war, 326outer core, 222overdamping, 144oxidation, 257oxygen transport, 257ozone, 250ozone depletion, 257

p-n junction, 199Pentek, Aron, 342pacemaker, 95, 145

INDEX

INDEX

paleomagnetic recording, 222Pan, 158pandemic, 281Pandora, 159Paola, C., 122Pappas, George, 344Papua New Guinea, 296parametric excitation, 165parsnip webworm, 322Pasta, John, 152Pastinaca sativa, 322peak oil theory, 6pedal locomotion, 171Pella-Tomlinson model, 23Peloponnesian war pestilence, 310pelota ball, 175pendulum

damped, 143double, 166inverted, 150marble, 165spherical, 165

pendulum period, 142percolation, 124perihelion, 157period doubling, 11, 76, 199, 229period-I,llperiod-2, 11period-3, 91period-n, 58permeability, 209permittivity, 209peroxidase-oxidase reaction, 277Peters, Randall, 188Pflug, Michael, 343pH regulation, 302phase plane, 36phase-plane analysis, 40phase-plane portrait, 40phenanthroline ferrous sulfate, 263phenylalanine hydroxylase, 257phenylketonuria, 257Physics World, 176picosecond pulse, 209piecewise linear, 196

379

ping pong ball, 175PITCHf/x, 180PKU, 257plague of Justinian, 310Planck's constant, 204plant-herbivore interaction, 322plant-pathogen interaction, 322plasma double layer, 123plate flutter, 201Poincare section, 58Poincare theorem, 40, 102Poincare-Bendixson theorem, 51, 274point

fixed, 36grid, 37ordinary, 36stationary, 36

point shaving, 192Poisson's equation, 63, 243polarization, 209polio epidemic, 309poloidal field, 224Pontryagin's maximum principle, 68Pontryagin, Lev, 68population growth

Malthus, 5Verhulst, 5

potassium-40, 224power spectrum, 60, 68, 151Prandtl number, 53predator-prey map, 92prejudice reduction, 128Prigogine, Ilya, 266primordial soup, 278prion, 296

normal, 297rogue, 297

prion protein cellular, 297prison sentences, 343prisoner's dilemma, 343privateer, 32probability density function, 246product adoption, 97Prometheus, 159proportional feedback, 89

380

Protopopescu, Vladimir, 342protozoa, 282Prouty, Raymond, 140pump beam, 216

Q machine, 201quantum mechanical tunneling, 199quasi-species model, 278

Rossler attractor, 67rabbit calcivirus, 23rabies transmission, 292rabies wavefront, 295radiative heat wave, 124radiosonde, 236Rand Corporation, 343random number generator, 87Rasmusen, Eric, 323rate constant, 255rats, 292rats and cats, 36Rayleigh number, 53Rayleigh-Benard convection, 271reaction-diffusion equation, 269Realtree Masterbucks, 188reduced mass, 156Rees, Gareth, 187refractory time, 122, 268relative vorticity, 237relaxation oscillation, 201, 203removed, 283replacement number, 285reservoir, 282resistor, 194resonance curve

linear, 153nonlinear, 154

resource competition, 25return speed, 164Reynolds number

bacterium, 132blood flow, 132drag force, 132dragonfly, 132fastball, 180

INDEX

large ship, 132magnetic, 224softball, 132sperm, 132swimmer, 132whale, 132

Reynolds, Osborne, 131ribonucleic acid, 278Riccati ODE, 61Richards, Diana, 323Richardson, Lewis Fry, 236, 324Ricker's model, 93ring of fire, 222RK4 algorithm, 16RKF45 algorithm, 20, 40RNA chemistry, 278RNA World, 278Roberts, Paul, 225Robey, Travis, 343roll response, 170rotor speed, 140round-off error, 109roundworm, 282Rowlands, George, 101Rules of Golf, 183Runge-Kutta algorithm, 16Russell, John Scott, 101

Saccharomyces cerevisiae, 5saddle point, 37salicylic acid, 257San Marco attractor, 92sand piles, 128Saperstein, Alvin, 327Sarajevo, 326Sastry, Shankar, 344saturable Lotka-Volterra model, 64Saturn's F ring, 159Saturn's rings, 158SBS, 216Scafetta, Nicola, 171Schizosaccharomyces kephir, 22Schnakenberg reaction, 275scrapie, 297search time, 314

INDEX

Seattle Mariners, 178second harmonic generation, 232second law, 30secular term, 154, 157SEIR model, 309Sel'kov, E. E., 273selection and evolution, 278self-replicate, 278self-similar, 67separating variables, 4separatrix, 106separatrix trajectory, 106, 270SGE, 105sheep blowfly, 24Shell Exploration, 6Shenoy, Ajay, 342shepherd moons, 159short oval, 189sidespin, 179, 182Sienkiewicz, Joe, 245Sierpinski's gasket, 67signal beam, 216silicon chip technology, 170Silver, Arnold, 208similarity solution, 108, 124simple harmonic oscillator, 31simple pendulum, 141simply connected region, 51sine map, 91sine-Gordon

algorithm, 115equation, 105mechanical model, 123solitary wave, 105

ski jumping, 69slab pulling, 222slapshot, 175smash, 175sockeye salmon, 93softball, 132solar irradiance, 252solar racer, 137Solenopsis invicta, 337solitary internal waves, 128soliton

antikink, 104bright, 213collision, 104dark, 213ion acoustic, 123kink, 104Korteweg-deVries, 101, 103nontopological, 100spherical, 213Toda, 168topological, 100

spaghetti plot, 246Spanish flu, 281Spanish flu epidemic, 309specific heat, 63speed of light, 156speedway oval, 190spermatozoa, 275spike, 175spin, 138spiral wave, 268spring

hard, 30, 148soft, 30, 148

spring constant, 30spruce budworm, 12, 275SQUID, 208, 229SQUID magnetometer, 208stability, 38stability criterion

Courant, 124Courant-Friedrich-Lewy, 251Von Neumann, 117

standard form, 36standard gravity, 243standard map, 97, 167stationary point, 36STBS, 216Stefan-Boltzmann law, 252Stepanek, Antonin, 138stimulated Brillouin scattering, 216Stoicheff, Boris, 216Stokes's resistance law, 54Stokes, George, 134, 213Strait of Gibraltar, 128

381

382

strange attractor, 54butterfly, 54double scroll, 199Henon, 90

stream function, 243stream lines, 243subduction, 222subharmonics, 58Sullivan, Eamon, 164Sulu sea, 128superconductor, 203supercurrent, 203supersonic flight, 169surface gravity wave, 101surface roughness, 133susceptibles, 283swarming theory, 342symbiosis, 23symbiotic interaction, 64synchronization, 145

menstrual cycle, 145

Taga, Gentaro, 171tangent field, 37tangent plane approximation, 237tapeworm, 282Tappert, Fred, 210target pattern, 268Taricha granulosa, 312Taubenberger, Jeffer~ 309Taylor expansion, 109, 149technology diffusion, 97Tenmile, Oregon, 313tennis ball, 138, 173tent map, 95terminal velocity, 134test tube experiment, 5tetanus toxin, 313tetrodotoxin, 313Texada Island, B.C., 314Thamnophis sirtalis, 312theorem

Poincare-Bendixson, 274thermal wind, 250thin liquid film, 108

INDEX

three-wave problem, 229Thrymr, 158Thunnus albacares, 23tiger stripes, 272time delay, 13time series, 87tin

disease, 256gray, 256leprosy, 256pest, 256white, 256

Titan, 158Toda lattice, 152Toda soliton, 168Toda, Morikazu, 152Tomlin, Claire, 344topspin, 179toroidal field, 224Tournament of France, 176Townes, Charles, 216toy model, Saturn's rings, 158trade barriers, 343traffic flow, 125trajectory

chaotic, 162quasi-periodic, 162separatrix, 102

troposphere, 236truncation error, 109Tschirnhaus, Ehrenfried, 34Tsuchiya, Kazuo, 171Tsujita, Katsuyoshi, 171TTX, 313Tucker, Albert, 343Tug Wajale, Somalia, 288tunnel diode, 228tunnel diode oscillator, 199turbulence, 133Turing, Alan, 271two-soliton solution, 124

u.S. Geological Survey, 6U.S. Golf Association, 183U.S. Navy Historical Center, 281

INDEX

Ulam, Stan, 119, 152Ulanowicz, Robert, 257ultimate oil recovery, 6unaimed fire, 335underdamping, 144unimodal map, 77Union army, 341United Kingdom, 327universal joint, 30universal sequence, 95University of Alaska Geophysical Insti-

tute, 233urea, 261US-48, 6USSR, 327

vaccination, 291Van Ark, James, 307van der Pol equation, 201van der Pol, Balthasar, 201Vancouver Winter Olympics, 245variable step method, 20vascular, 301vector, 282vector potential, 219, 229Verhulst ODE, 5vinegar, 257virus, 282viscosity coefficient, 134Vitagliano-D'Errico model, 297volleyball, 175Volterra, Vito, 16von Neumann, John, 236, 323vortex point, 37

Waage, Peter, 255Walmart, 8Waltman, Paul, 314war arrow, 187war chest, 323water vapor, 250wave

ion acoustic, 101solitary, 102spiral, 268

surface gravity, 101wave number, 210Weather Channel, 245weather chart

500-mbar, 245weather forecasting

rules of thumb, 251West, Bruce, 171white dwarf stars, 24wild parsnip, 322wind

geostrophic, 250gradient, 250katabatic, 250thermal, 250

wind tunnel, 140, 173wind turbine, 139

horizontal axis, 140vertical axis, 140

winding number, 96windows of periodicity, 11wing rock, 168wing span, 139Wolfers, Justin, 192Wolfram, Stephen, 119world food supply, 5worm-like locomotion, 171

yellowfin tuna, 23Yersinia pestis, 292Ymir, 158youtube, 250

Zabusky, Norm, 110zebra stripes, 272Zeidis, Igor, 171Zeitgebers, 145zeroth law, 152Zimmermann, Klaus, 171

383