Consider a model for the population P(t) of the fishery at time t with a constant harvest dP / dt = -(P-1) (P-4), P(0) = Po Where Po is the initial value. (a) Draw the phase portrait of the model (b) Determine the stability of all equilibria (c) Use the phase portrait to determine lim t - infinity P(t) in the cases when Po > 4, 1 < Po < 4, and 0 < Po < 1, respectively. Do not solve the equation.

Question

Consider a model for the population P(t) of the fishery at time t with a constant harvest

dP / dt = -(P-1) (P-4), P(0) = Po

Where Po is the initial value.

(a) Draw the phase portrait of the model

(b) Determine the stability of all equilibria

(c) Use the phase portrait to determine lim t - infinity P(t) in the cases when Po > 4, 1 < Po < 4, and 0 < Po < 1, respectively. Do not solve the equation.

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Math
Advanced Math

Differential Calculus