Suppose that a fish population P(t) (in thousands of fish) experiences logistic growth with rate r...

 

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Suppose that a fish population P(t) (in thousands of fish) experiences logistic growth with rate r per year and carrying capacity K (thousand) but is harvested continuously at rate h (thousand) per year. (a) If the population at t=0 is Po (thousand), explain the contribution of each term in the initial value problem dP dt P(0) = Po. P (-2) 1- T P-h, (b) Suppose that r = 4 per year and K = 4 (thousand) fish. Use the phase diagram concept in the case h = 3 and h = 8 (thousand) per year. Interpret the behavior of the system in both cases, and explain how they are different. (c) Identify the value of h where this difference occurs. Suppose that a fish population P(t) (in thousands of fish) experiences logistic growth with rate r per year and carrying capacity K (thousand) but is harvested continuously at rate h (thousand) per year. (a) If the population at t=0 is Po (thousand), explain the contribution of each term in the initial value problem dP dt P(0) = Po. P (-2) 1- T P-h, (b) Suppose that r = 4 per year and K = 4 (thousand) fish. Use the phase diagram concept in the case h = 3 and h = 8 (thousand) per year. Interpret the behavior of the system in both cases, and explain how they are different. (c) Identify the value of h where this difference occurs.