Example: The fox squirrel is a small mammal native to the Rocky Mountains. These squirrels are very territorial. Note the following observations:
.
Answer:
Clearly, we have P=0, P=N, and P=M. Using the graph of ,
we get the phase-line of the equilibrium points,
We conclude that P=0 and P=N are sinks, while P=M is a source.
,
where E > 0. Clearly, the graph of the function
can be obtained by shifting the graph of
down E-unit along the vertical axis. Clearly we have three cases according to the value of E and the value of f at the local maximum :
Clearly, the bifurcation is happening when E=f(h).