Curriculum Vitae“Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits”, D.V. Senthilkumar, K. Srinivasan, K. Murali, M. Lakshmanan

Curriculum Vitae

Name : Dr. K. SRINIVASAN

Assistant Professor

Department of Physics

Nehru Memorial College (Autonomous)

Puthanampatti 621 007

Tiruchirappalli (Dt), Tamilnadu, India

Phone : +91-4327 – 234 327

Fax : +91-4327 – 234 811

Mobile : 09994192433

e-mail : [email protected]

[email protected]

Academic Qualifications:

Degree Name of Institute Year of

Passing

Class Subject

Ph.D.

M.Sc.

B.Sc.

National Institute of Technology (NIT),

Tiruchirappalli-620 015, India

Bharathidasan University,


Bharathidasan University,


2009

2002

2000

First Class

(72.3%)

First Class

(62.7%)

Physics

Physics

Physics

Ph.D Thesis

Title of the Thesis : Bifurcations, Chaos and Strange Nonchaos in Certain

Nonautonomous Nonlinear Circuits

Place : Department of Physics

National Institute of Technology (NIT)

Tiruchirappalli - 620 015, India

Research Supervisor : Prof. D. Sastikumar

Duration : July 2004 – August 2009

Research Projects

Sl. No. Funding agency Title of the Project Amount

INR.

Tenure

1.

2.

DST-SERB FAST TRACK -

YOUNG SCIENTISTS,

Department of Science and

Technology (SERB-DST),

Govt. of India.

National Doctoral Fellow

(NDF), All India Council

for Technical Education

(AICTE), Govt. of India.

Design and study of regular

and delayed chaotic circuits

for emergent nonlinear

phenomena

Controlling and

Synchronization of chaotic

nonlinear circuit networks

24,65,000/-

5,67,000/-

2014 - 2017

2004-2008

Position Held

Teaching Experience

Assistant Professor in Physics, Nehru Memorial College, Puthanampatti since 19 May 2014.

Research Experience

Years of Experience : 11 years (01.05.2002 – present)

Post Doctoral Research : More than Four Years

During Ph.D : Five Years

Pre Doctoral Research : Two Years

1. Designation : Scientist

Research Supervisor : Prof. M. Lakshmanan

Place : Centre for Nonlinear Dynamics, School of Physics,

Bharathidasan University, Tiruchirappalli, India

Title : Nonlinear Dynamics – Chaotic Circuits

Sponsored : Department of Science and Technology (DST),

Government of India

Duration : 29 November 2011 – 16 May 2014

2. Designation : Research Associate (RA)






Government of India

Duration : 26 October 2010 – 28 November 2011

3. Designation : Senior Research Fellow (SRF)






Government of India

Duration : 16 February 2009 – 25 October 2010

4. Designation : National Doctoral Fellow (NDF)

Research Supervisor : Prof. D. Sastikumar

Place : Department of Physics, National Institute of Technology,

Tiruchirappalli, India

Title : Controlling and Synchronization of chaotic nonlinear circuit

networks

Sponsored : All India Council for Technical Education (AICTE),

Government of India

Duration : November 2004 - November 2008

5. Designation : Project Assistant (PA)

Place : Department of Physics, National Institute of Technology,

Tiruchirappalli, India

Title : Bifurcation and chaos in periodically pulsed nonlinear

electronic circuits – application to chaotic cryptography and

secure communication

Sponsored : Defence Research & Development Organization (DRDO),

Government of India

Duration : October 2002 - October 2004

Academic Honours/Awards

1. Prof. R. Ranganathan award for the top score in Mathematical Physics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, India (Year 2002)

2. Prize for college first in M.Sc., program, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, India (Year 2002)

3. Dr. C. Naivar Mohamed endowment award for the topper in the M.Sc., Physics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, India (Year 2003)

4. Prof. R. Ranganathan endowment award for the topper in the M.Sc., Physic, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, India (Year 2003)

5. National Doctoral Fellowship (NDF) awarded by All India Council for Technical Education, New Delhi, India (Year 2004).

6. Senior Research Fellow (SRF), Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, India (Year 2009)

7. Research Associate (RA), Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, India (Year 2010)

8. Scientist, Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, India (Year 2011)

9. Young Scientist award of SERB-DST Fast Track (Year 2014)

Research Supervision

Working Completed

Ph.D

M.Phil 3

Publications

List of Publications in Refereed International Journals

1. “Multiple period-doubling bifurcation route to chaos in periodically pulsed chaotic oscillators”, S. Parthasarathy and K. Srinivasan, Proc. of Dynamic Systems and

Applications 4, 52-60 (2004)

2. “Multiple period doubling bifurcation route to chaos in periodically pulsed Murali-

Lakshmanan-Chua (MLC) circuit”, K. Srinivasan, Int. J. Bifurcation and Chaos 18,

541-555 (2008)

3. “Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force”, D.V. Senthilkumar, K. Srinivasan, K. Thamilmaran and M.

Lakshmanan, Phys. Rev. E 78, 066211(10) (2008)

4. “Effect of nonsinusoidal periodic forces in Duffing oscillator: Numerical and analog simulation studies”, K. Srinivasan, K. Thamilmaran and A. Venkatesan, Chaos,

Solitons & Fractals 40, 319-330 (2009)

5. “Classification of bifurcations and chaos in Chua's circuit with effect of different periodic forces”, K. Srinivasan, K. Thamilmaran and A. Venkatesan, Int. J. Bifurcation

and Chaos 19, 1951-1973 (2009)

6. “Experimental realization of strange nonchaotic attractors in a nonlinear series LCR circuit with nonsinusoidal force”, K. Srinivasan, D.V. Senthilkumar, R. Suresh, K.

Thamilmaran and M. Lakshmanan, Int. J. Bifurcation and Chaos 19, 4131–4163 (2009)

7. “Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits”, D.V. Senthilkumar, K. Srinivasan, K. Murali, M. Lakshmanan and

J. Kurths, Phys. Rev. E (Rapid Communication) 82, 065201 (2010)

8. “Design of time delayed chaotic circuit with threshold controller”, K. Srinivasan, I. Raja Mohamed, K. Murali, M. Lakshmanan and Sudeshna Sinha, Int. J. Bifurcation and

Chaos, 21, 725-735 (2011)

9. “Observation of chaotic beats in a driven memristive Chua's circuit”, A. Ishaq Ahamed, K. Sinivasan, K. Murali and M. Lakshmanan, Int. J. Bifurcation and Chaos, 21, 737-

757 (2011)

10. “Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity”, K. Srinivasan, D.V. Senthilkumar, K. Murali, M. Lakshmanan and J.

Kurths, CHAOS, 21, 023119 (2011)

11. “Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua’s circuits without delay”, K. Srinivasan, D.V. Senthilkumar, I. Raja

Mohamed, K. Murali, M. Lakshmanan and J. Kurths, CHAOS 22, 023124 (2012)

12. “Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits”, R. Suresh, K. Srinivasan, D.V. Senthilkumar, I. Raja Mohamed, K. Murali, M.

Lakshmanan and J. Kurths, European Physical Journal Special Topics 222, 729-744

(2013)

13. “Dynamic environment coupling induce synchronized states in coupled time-delayed

electronic circuits” R. Suresh, K. Srinivasan, D.V. Senthilkumar, K. Murali, M.

Lakshmanan, J. Kurths, Int. J. Bifurcation and Chaos 24, (2014) (Accepted)

14. “Different types of synchronization in coupled network based chaotic circuits” K. Srinivasan, V.K. Chandrasekar, R. Gladwin Pradeep, K. Murali and M. Lakshmanan,

Commun Nonlinear Sci Numer Simul (submitted)

15. “Synchronization, phase-flip transition and amplitude death in delay-coupled nonlinear electronic circuits” B. Akila, K. Srinivasan, P. Muruganandam and K. Murali, Commun

Nonlinear Sci Numer Simul (submitted)

16. “Duffing-Van der Pol oscillator type dynamics in Murali-Lakshmanan-Chua (MLC) circuit”, K. Srinivasan, V. K. Chandrasekar, I. Raja Mohamed and A. Venkatesan,

Chaos, Solitons & Fractals (submitted)

List of Publications in Refereed International Conference Proceedings

17. “Bifurcation and chaos in MLC circuit with simple nonlinearity”, K. Srinivasan, K. Thamilmaran and A. Venkatesan, Nonlinear dynamics : concepts and applications

edited by M. Daniel and S. Rajasekar (Narosa 2009) pp. 319

18. “Lag and anticipating synchronization in one way coupled Chua's circuit”, I. Raja Mohamed and K. Srinivasan, IEEE Proc. of Devices, Circuits and Systems (ICDCS), 2014

19. “Simple nonautonomous Wien-bridge oscillator based chaotic circuit”, R. Rizwana, I. Raja Mohamed, K. Srinivasan and M. Inbavalli, IEEE Proc. of Devices, Circuits and

Systems (ICDCS), 2014

20. “Phase-flip transition in coupled time-delayed piecewise linear electronic circuits” B. Akila, K. Srinivasan, P. Muruganandam and K. Murali, IEEE Proc. of Devices, Circuits and

Systems (ICDCS), 2014

List of Publications in Refereed National Conference Proceedings

21. “Multiple period-doubling bifurcation route to chaos in periodically pulsed Morse oscillator”, K. Srinivasan and S. Parthasarathy, Proc. of Second National Conference on

Nonlinear Systems & Dynamics – NCNSD 2005

Presented at Conferences and Workshops

22. “Synchronization transitions in chaotic time-delay electronic circuits”, K. Srinivasan, D. V. Senthilkumar, K. Murali , M. Lakshmanan and J. Kurths, presented at the sixth

National Conference on Nonlinear Systems and Dynamics (NCNSD-2011)

Presentation/Participation in Conferences/Workshops

1. Participated in the winter School on Nonlinear Optics : Theory and Applications organised by the Centre for Nonlinear Dynamics, Bharathidasan University, Trichy –

620 024 during December 1-13, 2003.

2. Participated in the summer School 2004 from May 31st – June 5th, 2004 organized by Nonlinear Studies Group, IISC, Bangalore – 560012.

3. Participated in the second National Conference on Nonlinear Systems and Dynamics held at Department of Physics, Aligarh Muslim University, Aligarh, Delhi during 24-26

February, 2005.

4. Participated in the workshop on Mathematical Neurosciences – An Introduction on July 27, 2005 organized by Nonlinear Studies Group, IISc, Bangalore – 560012.

5. Participated in the workshop on Optics & Photonics (WOOP-2005) held on 18, 19 August 2005 organized by Department of Physics, NIT, Trichy – 620 015.

6. Participated in the seminar on Recent Developments in Physics conducted by School of Physics, Bharathidasan University, Trichy – 620024 during 21-22, November 2005.

7. Participated in the second DST SERC School on Nonlinear Dynamics held at Pondicherry University, Pondicherry, January 04-24, 2006.

8. Participated in the third National Conference on Nonlinear Systems and Dynamics (NCNSD- 2006), The Ramanujan Institute for Advanced Study in Mathematics,

University of Madras, Chennai - February, 2006.

9. Participated in the workshop on communication skills conducted by Department of Physics, NIT, Trichy – 620015 on December 01, 2006.

10. Participated in the workshop on Laser materials processing (LAMP – 2007) on 9 & 10, January 2007 in National Institute of Technology, Trichy – 620 015.

11. Participated in the workshop on High performance Computing held during August 6-9, 2007 organized by Centre for Nonlinear Dynamics, School of Physics, Bharathidasan

University & C-DAC, Pune.

12. Participated in the two day workshop on computational fluid dynamics on 17 & 18 September, 2007 at Department of Mathematics, National Institute of Technology,

Trichy – 620 015.

13. Participated in the workshop on Advanced Materials & Devices on 10th January, 2008 at Department of Physics, National Institute of Technology, Trichy – 620015.

14. Participated in the workshop on Advanced Coating Technologies and their Applications on 24th January 2008 at Department of Physics, National Institute of Technology, Trichy

– 620015.

15. Participated in the lecture workshop of frontier topics in physics on 4 & 5, February 2008 organized by Department of Physics, Bishop Heber College, Trichy – 620 017.

16. Participated in the International Conference on Recent developments in nonlinear dynamics organized at the Centre for Nonlinear Dynamics, School of Physics,

Bharathidasan University, Trichy – 620 024 during 12-16, February 2008.

17. Participated in the workshop on Nanostructures and devices on 23 February, 2008 at Department of Physics, National Institute of Technology, Trichy – 620 015.

18. Participated in the seminar on Frontier topics in fundamental physics on March 30-31, 2009 at School of Physics, Bharathidasan University, Trichy – 620 024.

19. Participated in the DST SERC School on Nonlinear Dynamics held at Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirappalli, January 04-26, 2011.

20. Participated in the NMI Workshop on Nonlinear integrable systems and their applications held at Centre for Nonlinear Dynamics, Bharathidasan University,

Tiruchirappalli, February 24- March 01, 2014.

Research Interests

Nonlinear Dynamics - Theory and Electronic Experiments

Chaotic Circuit Design

Nonlinear Systems Modeling

Discrete and Time-Delay Dynamical Systems and Circuits

Synchronization of Chaos

Strange Nonchaotic Attractors

Computer Skills

Programming experience in FORTRAN 77, 90/95, C and C++

Experience in using scientific and symbolic packages like MATLAB and

MATHEMATICA

Typesetting and Plotting packages : LaTex, Gnuplot

Operating systems : Linux, Windows

Simulation Tools : Pspice, Electronic workbench, Circuit maker.

Statement about scientific contribution : See Annexure

Reference

1. Prof. M. Lakshmanan, D.Sc.(h.c), F.N.A.Sc., F.A.Sc., F.N.A, F.TWAS. Professor of Eminence & DAE Ramanna Fellow

Centre for Nonlinear Dynamics

School of Physics

Bharathidasan University

Tiruchirapalli-620 024, India

Email : [email protected] / [email protected]

Phone/Fax : +91-(0)431-2407093

2. Prof. Sudeshna Sinha F.A.Sc.

Head, Department of Physical Science

Indian Institute of Science Education and Research (IISER), MOHALI

Knowledge City, Sector 81

Sas Nagar, Manauli PO 140306

India


Tel: +91-172-0172-2688466

3. Prof. K. Murali Department of Physics

Anna University

Chennai – 600025, India


Tel: +91-(0)44-2235 8692

4. Prof. M. Daniel Head

Centre for Nonlinear Dynamics

School of Physics

Bharathidasan University

Tiruchirapalli-620 024, India


Phone: +91-(0)431-2407057

Fax : +91-(0)431-2407093

A brief summary of Ph.D research

In this thesis a systematic study of bifurcations and chaotic phenomena in certain generalized nonlinear

oscillators driven by different external periodic and quasiperiodic forces is studied. In particular, two

different kinds of dynamical systems are studied, namely (1) nonlinear oscillators subjected to different

types of external periodic forcing, and (2) nonlinear oscillators subjected to two-frequency

quasiperiodic forcing. Further the dynamics in a one or two-parameter space in the above mentioned

systems is investigated. It has been shown that these systems exhibit a rich variety of bifurcations,

regular and complex structures including strange chaotic and nonchaotic behaviour. Specifically, we

consider the following class of nonlinear dynamical systems, namely periodically forced Duffing

oscillator, Chua's circuit, Murali-Lakshmanan-Chua (MLC) circuit, and MLC circuit with simple

nonlinearity, for our investigations. Detailed analysis on each of the cases is carried out and the results

are presented with reference to a one or a two-parameter bifurcation diagrams. The details are

highlighted in the following fashion.

Multiple period doubling bifurcation route to chaos The effect of additional periodic forces in the MLC circuit is studied. The additional periodic forces of

pulse type display novel dynamical features including multiple period doubling bifurcation route to

chaos, followed by a rich variety of dynamical phenomena including enlarged periodic windows,

attractor crises, distinctly modified bifurcation structures and so on. For certain types of periodic

pulses, the circuit also admit transcritical bifurcation preceding the onset of multiple period doubling

bifurcations. Characterization of the numerical simulation results is done using Lyapunov exponents,

correlation dimension and power spectrum, which are found to be in good agreement with the

experimental observations. It is shown that the chaotic attractor becomes more complicated and their

corresponding return maps are no longer simple for large n-periodic pulses, which has a lot of potential

applications in secure communication. The above study also indicates that one can generate any

desired n-period doubling bifurcation behaviour by applying n-periodic pulses to a chaotic system.

Finally, we study the Duffing oscillator with a single well potential with the addition of the above

periodic pulses which also exhibits the aforementioned novel behaviour.

Nonlinear electronic circuit with diode based nonlinearity A simple nonautonomous circuit exhibiting regular as well as chaotic behaviour is constructed. It is

well known MLC circuit with a simple nonlinear element. This circuit admits the familiar double

scroll type attractor of the MLC circuit and also the Duffing van der Pol circuit type chaotic attractors

for suitable parameter values. It is interesting to note that depending on the circuit parameters, the

system exhibits both period doubling bifurcation route to chaos and quasiperiodic route to chaos. The

dynamics is studied by using hardware implementation and numerical analysis. The results are also

confirmed by explicit segment-wise analytical studies. Particularly, we construct two-parameter

bifurcation diagrams in the forcing amplitude-frequency plane,

numerically.

Effect of different periodic forces in certain chaotic circuits The effect of different periodic excitations like sine, square, triangle and sawtooth waves on the Chua's

circuit is considered and it is shown that the circuit can undergo distinctly modified bifurcation

structure, generation of new periodic regimes, induction of crises and so on. The dynamics is studied

numerically using phase portrait, two-parameter bifurcation diagram, one parameter bifurcation

diagram, Lyapunov exponents and basin of attractor with different initial conditions. Most of these

numerical studies are in close agreement with the observation from hardware experiments. Finally, the

effect of different periodic forced Duffing oscillator with a single well case is also studied numerically

and analog circuit simulation methods. The dynamics of the MLC circuit and the MLC circuit with

diode based nonlinearity under the influence of different periodic forces is also studied. It is shown

that the system exhibits rich variety of dynamical phenomena. An interesting symmetry in the

dynamics is captured by varying the duty cycle of square wave as a control parameter. Controlling of

chaos is also shown by employing dc offset voltage as a parameter.

Strange nonchaotic attractors in nonlinear electronic circuits Strange nonchaotic attractor (SNA) in a quasiperiodically forced negative conductance series LCR

circuit with a diode under nonsinusoidal force as one of the quasiperiodic forces. A new route for the

birth of SNA, namely, bubbling route, besides the other prominent routes, such as fractalization,

fractalization followed by intermittency, intermittent and the Heagy-Hammel routes is identified for

the first time. The birth of SNAs by these routes are characterized from both the experimental and

numerical data by the maximal Lyapunov exponents and their variance, Poincare maps, Fourier

amplitude spectrum, spectral distribution function and the distribution of finite-time Lyapunov

exponents.

Controlling of chaos in certain chaotic circuits Controlling of chaos using various non-feedback methods is described. Here, controlling of chaos is

achieved in the MLC circuit and also in the Duffing oscillator with the addition of one more different

weak periodic force. These systems indeed exhibit chaotic behaviour in the absence of the second

periodic signal. However, the effect of the second periodic signal and for a certain range of values of

amplitude and frequency, the initial chaotic motion is completely eliminated or controlled into a

periodic one. Finally controlling of chaos is shown by addition of constant bias/offset voltage on the

MLC circuit and the Duffing oscillator, numerically. These systems alter chaotic dynamics to any

desired periodic dynamic through reverse period doubling bifurcation when the control parameter is

varied.

A Detailed Description of Scientific Contributions

Design of time delayed chaotic circuit with threshold controller A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors

is designed. This circuit consists of only a few operational amplifiers and diodes and employs a

threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of

piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by

constructing the phase portraits of the attractors through numerical simulations and hardware

experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors

by just introducing more number of threshold values.

Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic

circuits We report the experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally

coupled time-delay systems using electronic circuits. We have also implemented experimentally an

efficient methodology for characterizing CPS, namely, the localized sets. Snapshots of the evolution of

coupled systems and the sets as observed from the oscilloscope confirming CPS are shown

experimentally. Numerical results from different approaches, namely, phase differences, localized sets,

changes in the largest Lyapunov exponents, and the correlation of probability of recurrence corroborate

the experimental observations.

Synchronization transitions in coupled time-delay electronic circuits with a threshold

nonlinearity Experimental observations of typical kinds of synchronization transitions are reported in

unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time

delays, namely feedback delay tau1 and coupling delay tau2 . We have observed transitions from

anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and

inhibitory couplings, respectively, as a function of the coupling delay tau2 . The anticipating and lag

times depend on the difference between the feedback and the coupling delays. A single stability

condition for all the different types of synchronization is found to be valid as the stability condition is

independent of both the delays. Further, the existence of different kinds of synchronizations observed

experimentally is corroborated by numerical simulations and from the changes in the Lyapunov

exponents of the coupled time-delay systems.

Anticipating, complete and lag synchronizations in RC phase-shift network based coupled

Chua’s circuits without delay We construct a new RC phase shift network based Chua’s circuit, which exhibits a period-doubling

bifurcation route to chaos. Using coupled versions of such a phase-shift network based Chua’s

oscillators, we describe a new method for achieving complete synchronization (CS), approximate lag

synchronization (LS), and approximate anticipating synchronization (AS) without delay or parameter

mismatch. Employing the Pecora and Carroll approach, chaos synchronization is achieved in coupled

chaotic oscillators, where the drive system variables control the response system. As a result, AS or LS

or CS is demonstrated without using a variable delay line both experimentally and numerically

Observation of chaotic beats in a driven memristive chua’s circuit A time varying resistive circuit realizing the action of an active three segment piecewise linear flux

controlled memristor is proposed. Using this as the nonlinearity, a driven Chua’s circuit is

implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of

parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less

conductive OFF state and a more conductive ON state. This chaotic switching is governed by the

dynamics of the driven Chua’s circuit of which the memristor is an integral part. The occurrence of

beats is essentially due to the interaction of the memristor aided self-oscillations of the circuit and the

external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor

switching and that of the external force, constructive and destructive interferences occur leading to

revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical

simulations and Multisim modeling as well as statistical analyses have been carried out to observe as

well as to understand and verify the mechanism leading to chaotic beats.

Current assignment and nature of work

We have constructed the family of Murali-Lakshmanan-Chua circuit like circuits. We have obtained

some interesting experimental results for that circuit. For this simple and interesting nonlinear

nonautonomous chaotic circuit we deduced the equations of motion which we have numerically

studied. The nature of the dynamics is studied using phase portrait, two parameter bifurcation diagram,

one parameter bifurcation diagram and the results and then confirmed with experimental circuit

realization. We have observed several bifurcation and chaotic phenomena.

A novel delayed chaotic oscillator exhibiting mono and two scroll complex hyperchaotic attractor is

constructed. The designed circuit consists of a few operation amplifiers and diodes and by employing

threshold controller the break down voltage of piece wise linear function is varied. The control of

piece wise linear function facilitates controlling the shape of attractors. This is shown using phase

portraits of the attractors both numerically and experimentally.

We have systematically studied different synchronization of coupled chaotic delayed circuit both

numerical and experimental realizations. We have observed amplification of chaotic attractor in a

coupled delayed chaotic system. We identified synchronizations of chaotic system namely, complete

synchronization, Lag synchronization, Anticipating synchronization, phase synchronization, inverse

synchronization and than oscillating synchronization observed experimentally.

I am working towards identifying potential application of this delay circuit. We have also planned to

work on coupled delay circuits, network analysis (small world network) and application of secure

communication and cryptography.

Work to be carried out

Several new simple and robust chaotic circuits will be constructed and their dynamics and characterization will be studied. Next we have to design the nonlinear circuits containing

oscillator and nonlinearity with filter. We have to study their dynamical behaviour with effect of

various types of filter. Next this will be extended to the number of filter units in the circuit and

study their dynamics. Dynamics and application of network based chaotic circuits for different

types of synchronizations without delay time will be investigated. The concepts of parameter

mismatch between drive and response circuits, for both circuit systems exhibiting complete, lag

and anticipating synchronizations depending upon the parameter mismatch values without time-

delay units will be analyzed.

A novel time-delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors will be designed. Next, we will show the effect of threshold controller in producing

multi-scroll attractors in a time-delayed circuit for proper choice of the parameter values.

Threshold values x∗ for the amplitude of the modulating square wave exhibiting two single scroll chaotic attractors and two double scroll chaotic attractors will be analyzed. Similarly

multi-scroll chaotic attractors (n > 2) can also be observed by choosing more number of

threshold voltages. That is, one needs to carefully clip the threshold function into multiple

segments.

The effect of different periodic forces on the time-delay chaotic circuit with threshold nonlinearity will be our next focus. The different periodic excitations on the dynamics of time-

delay circuits will be studied numerically and experimentally. The same circuit can exhibit

strange nonchaotic attrcator (SNA) under the influence of different quasiperiodic forces.

We will concentrate on the demonstration of different types of chaotic and hyperchaotic synchronization in the coupled time-delay electronic circuits with threshold nonlinearity. We

will systematically analysis the time-delay circuit with different coupling techniques like

unidirectional error feedback coupling, nonlinear delay coupling, delay coupling, cascading

coupling, some simple and complicated engineering coupling, to show the existence of phase,

lag, anticipating, complete and so on.

We will extend this to network (small world) based time-delay circuit systems. Finally, we will analyse the synchronization in the coupled time-delay circuits for chaos based computation.

Documents

Curriculum Vitae“Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits”, D.V. Senthilkumar, K. Srinivasan, K. Murali, M. Lakshmanan