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A Two Stage Periodic Discrete Logistic Equation

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.

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A Two Stage Periodic Discrete Logistic Equation

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  1. 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

  2. The Discrete Logistic (DL) Equation

  3. Periodic DL Equation K(t) is p-periodic but not constant

  4. Periodic DL Equation - Properties All solutions tend to positive, p-period cycle. Average of pop. cycle < average of K-cycle

  5. Juvenile-Adult Version of DL equation

  6. Periodic Juvenile-Adult Version of DL equation

  7. 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?

  8. t 1 2 3 4 5 6 7 8 9 10 11 12 0 KA(t) L H L H L H L H L H L H L J(t) A(t) Graphical Model Investigation

  9. Numerical Simulations when KA has Period pK=2 pK=2 carrying capacity

  10. Numerical Simulations when KA has Period pK=3 pK=3 carrying capacity

  11. Juvenile – Adult Phase Plot Where pK=3 A(t) J(t)

  12. Numerical Simulations when KA has Period pK=4 pK=4 carrying capacity

  13. New Theorem (J0,A0)=(0,S) (J0,A0)=(R,S) pK 2 pA=2, Av(A)<Av(K) pA=2, Av(A)=Av(K) Odd pA=2pK, Av(A)<Av(K) pA=pK, Av(A)<Av(K) pA=pK, Av(A)<Av(K) pA=pK, Av(A)<Av(K) Even>2

  14. Next Steps Expand proof to more juvenile stages Iteroparity rather than Semelparity When do we get Av(A)>Av(K)?

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