A Two Stage Periodic Discrete Logistic Equation Zhen Chen - Univ. Western Ontario Jim Cushing - Univ. Arizona Edgar Delgado-Eckert - Virginia Tech. / Tech. Univ. Munich Matthew Smith - Heriot-Watt Univ. Edinburgh The Discrete Logistic (DL) Equation Periodic DL Equation K(t) is p-periodic but not constant Periodic DL Equation - Properties All solutions tend to positive, p- period cycle. Average of pop. cycle < average of K-cycle Juvenile-Adult Version of DL equation Periodic Juvenile-Adult Version of DL equation Periodic DL Equation Properties Reminder All solutions tend to positive, p- period cycle. Average of pop. cycle < average of K-cycle Do these properties also apply for periodic juvenile-adult version of DL model? Graphical Model Investigation t J(t) A(t) K A (t) HLHLHLHLHLHLL Numerical Simulations when K A has Period p K =2 p K =2 carrying capacity Numerical Simulations when K A has Period p K =3 p K =3 carrying capacity Juvenile Adult Phase Plot Where p K =3 J(t) A(t) Numerical Simulations when K A has Period p K =4 p K =4 carrying capacity New Theorem pKpK 2 Odd Even>2 ( J 0, A 0 )=(0,S)( J 0, A 0 )=(R,S) p A =2, Av(A)