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Math Help - Periodicity of Lotka-Volterra model

  1. #1
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    Periodicity of Lotka-Volterra model

    Hello,
    Is there a possibility to disorder the periodicity in some predator-prey model?
    I'm looking for some example.
    What is the reason that could cause the disorder?
    What about the system's behaviour after disordering its periodicity?

    Thanks...
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Two trivial cases:

    (a) In absence of predators: x'(t)=Ax(t)\;(A>0) .

    (b) In absence of preys y'(t)=-By(t),\;(B>0) .
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  3. #3
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    Thanks, FernandoRevilla.
    What about the systems behaviour?
    For example, in absence of predators, preys populaton will grow up exponentially. Does it mean that periodicity is disordered in that case?
    I'm not sure I understood correctly?!
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by tulipe View Post
    For example, in absence of predators, preys populaton will grow up exponentially.

    Yes, the solutions are x=Ce^{At} (non periodic). This is different from the standard model:

    \begin{Bmatrix} x'=(A-Cy)x\\y'=(Dx-B)y\end{matrix}\quad A,B,C,D>0

    whose orbits are closed (periodic solutions) with only one equilibrium point at (B/D,A/C) .
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  5. #5
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    Thanks again....
    You helped me a lot! :-)
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