Stats Solutions

(Step-by-Step) Consider the predator-prey model (dN)/(dt)=rN-c(N-S)P , (dP)/(dt)=b(N-S)P-mP , where N(t) is the size the prey population at time t, P(t)

Question: Consider the predator-prey model

\(\left\{ \begin{aligned} & \frac{dN}{dt}=rN-c\left( N-S \right)P \\ & \frac{dP}{dt}=b\left( N-S \right)P-mP \\ \end{aligned} \right.\)

where N(t) is the size the prey population at time t, P(t) is the size of the predator population at time t and S > 0 is a fixed amount of prey that may hide in a refuge to avoid predation. You may assume all other parameters r, c, b, m are positive constants.

a.) Non-dimensionalize the system.

Hint: List each parameter with units to make your choices for change of variable that nondimensionalizes the system. (See lectures from Feb 20 and Feb 22 for help.)

b.) Find the critical points of the non-dimensionalized system.

c.) Determine the stability of each critical point from part b.

d.) Use your analysis in part b and c to describe the critical points and stability of the original predator-prey model.

Price: $2.99
Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document


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