Differential Equations - Bifurcations

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The discussion focuses on finding the bifurcation value for the differential equation dS/dt=kS*[1-(S/N)]*[(S/M)-1], where K and M are constants and M is less than or equal to N. A bifurcation value indicates the parameter value at which the stability of an equilibrium point changes. The first step in this process involves determining the equilibrium points of the equation as a function of N, specifically by setting dS/dt to zero and solving for S. This analysis is crucial for understanding how equilibrium points interact and lead to bifurcations.

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torresmido
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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
 
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torresmido said:
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
 
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.
 

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