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Homework Statement
The following model describes a fox population:
[tex]\frac{dS}{dt} = kS(1 - \frac{S}{N})( \frac{S}{M} - 1)[/tex]
a) at what value of N does a bifurcation occur?
b) How does the population behave if the parameter N slowly and continouly decreases towards the bifurcation value?
Homework Equations
The Attempt at a Solution
a) Bifurcation occurs when [tex]\frac{dS}{dt} = 0[/tex] and in terms of N, it would be when N = S.
b) as N appraoches the bifurcation point, the population would also deacrese until it reaches S, at which point the population would be 0 (based upon the model)
Is that all?