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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- Mar 7th 2011, 07:47 AMtulipePeriodicity 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... - Mar 7th 2011, 08:06 AMFernandoRevilla
Two trivial cases:

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

**(b)**In absence of preys $\displaystyle y'(t)=-By(t),\;(B>0)$ . - Mar 7th 2011, 08:16 AMtulipe
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?! - Mar 7th 2011, 08:32 AMFernandoRevilla

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

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

whose orbits are closed (periodic solutions) with only one equilibrium point at $\displaystyle (B/D,A/C)$ . - Mar 7th 2011, 08:41 AMtulipe
Thanks again....

You helped me a lot! :-)