Suppose a ranch can sustain a herd of cattle and that the cattle population (P)

Question

Suppose a ranch can sustain a herd of cattle and that the cattle population (P) can be modeled by the logistic equation below. dp/dt=0.001(500-p)p where dP/dt is the rate of change in the number of head per year. a) determine the equilibrium states of this base model and label which are stable and unstable nodes. b) if we choose to sell one animal per week (52 / year), what is the new model? c) determine the new equilibrium states and describe them as stable or unstable. You may want to make a graphical representation of the two models to aid in your analysis.

Explanation / Answer

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a)dp/dt=0 then it is in equilibrium
.001(500-p)p=0
p=0,500 are the equilibrium states
for stable equilibrium d/dt(dp/dt)=+ve p=0 it is stable
for stable unstable equilibrium d/dt(dp/dt)=-ve p=500
b)dp/dt=.001(500-p)p-52
c)p=352;p=147 at p=352 it is unstable and

at p= 147 it is stable

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