If 4h D kM2, show that typical solution curves look as

Chapter , Problem 27

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If 4h D kM2, show that typical solution curves look as illustrated in Fig. 2.2.14. Thus if x0 = M=2, then x.t / ! M=2 as t ! C1. But if x0 < M=2, then x.t / D 0 after a finite period of time, so the lake is fished out. The critical point x D M=2 might be called semistable, because it looks stable from one side, unstable from the other.for a logistic population. At any lesserharvesting rate thepopulation approaches a limiting population N that is lessthan M (why?), whereas at any greater harvesting rate thepopulation reaches extinction.

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