Differential Equations - Bifurcations

[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

 

[LeBrad]

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

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

 

[HallsofIvy]

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.