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categoryرياضيات schoolبكالوريوس event_available2026-07-13

السؤال

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10. For a fish population modeled by a depensation growth model, we have, when there is harvesting, dt N= F(N)-H(N). where and H(N)=qEN. F(N) N (N/N-1)(1 - N/K) a. Find (and plot, freehand) the sustained yield H(N) as a function of effort E, and the unsustainable yield H(N2), also as a function of E (and plot on the same figure). Here N is the nontrivial stable equilibrium of N and N is the unstable equilibrium. b. Find the E(= Emax), where the two curves in (a) merge (this happens when N = N3). What happens to the fishery and the fish population when E Emax? === c. Suppose harvesting is done at effort level E = Emax for a while so that the fish population is below what was thought of as the "sustainable" N (which is equal to N₂, so actually it is not really sustainable). Realizing that there is a problem, the government puts in a fishing limit that reduces the effort E to slightly below Emax. Can the fishery recover?

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