# Differential Equations - Bifurcations

1. Feb 11, 2008

### torresmido

dS/dt=kS*[1-(S/N)]*[(S/M)-1]

Assume that K ans M are constans (where M is lower or Equal to N).
Find the bifurcation value for N?

I really didn't know where to start. Any help is appreciated

2. Feb 11, 2008

A bifurcation value is the parameter value at which the stability of an equilibrium point changes.

Step 1.) Find the equilibrium point(s) of the equation as a function of N. i.e., given a value of N, find S such that dS/dt = 0

3. Feb 11, 2008

### HallsofIvy

Staff Emeritus
It should be very easy to find the equilibrium points, one of which depends on the parameter N. "Bifurcation" happens essentially when one of the equilibrium points "runs into" another.