ricker, beverton-holt models

**ezong** · October 14th 2009, 07:59 PM

Ricker model
$\frac{dN}{dt}=\frac{rN}{e^{\beta N}}$

Beverton-Holt model
$\frac{dN}{dt}=\frac{rN}{\alpha +N}$

To get steady states, do I just set $\frac{dN}{dt}=0$ for both models?
I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?

**CaptainBlack** · October 15th 2009, 02:51 AM

Originally Posted by ezong

Ricker model
$\frac{dN}{dt}=\frac{rN}{e^{\beta N}}$

Beverton-Holt model
$\frac{dN}{dt}=\frac{rN}{\alpha +N}$

To get steady states, do I just set $\frac{dN}{dt}=0$ for both models?
I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?

Linearise about the steady state and either solve the linearised equation, if you have a growing solution you have instability. Alternativly just examin the linearised equation to determine the stability of the steady state.

In these cases the steady state appears to be $N=0$ , and for a small departure from the steady state the departure grows if $r>0$ and $r/\alpha>0$ respectivly.

CB

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