# Periodicity of Lotka-Volterra model

• Mar 7th 2011, 07:47 AM
tulipe
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...
• Mar 7th 2011, 08:06 AM
FernandoRevilla
Two trivial cases:

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

(b) In absence of preys $y'(t)=-By(t),\;(B>0)$ .
• Mar 7th 2011, 08:16 AM
tulipe
Thanks, FernandoRevilla.
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 AM
FernandoRevilla
Quote:

Originally Posted by tulipe
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 $(B/D,A/C)$ .
• Mar 7th 2011, 08:41 AM
tulipe
Thanks again....
You helped me a lot! :-)