Thread: ricker, beverton-holt models

1. ricker, beverton-holt models

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

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

To get steady states, do I just set $\displaystyle \frac{dN}{dt}=0$ 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?

2. Originally Posted by ezong
Ricker model
$\displaystyle \frac{dN}{dt}=\frac{rN}{e^{\beta N}}$

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

To get steady states, do I just set $\displaystyle \frac{dN}{dt}=0$ 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 $\displaystyle N=0$, and for a small departure from the steady state the departure grows if $\displaystyle r>0$ and $\displaystyle r/\alpha>0$ respectivly.

CB