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Harvesting a logistic population in a slowly varying environment. (English) Zbl 1229.92075
Summary: The classic problem for a logistically evolving single species population being harvested involves three parameters: rate constant, carrying capacity and harvesting rate, which are taken to be positive constants. However, in real world situations, these parameters may vary with time. This paper considers the situation where these vary on a time scale much longer than that intrinsic to the population evolution itself. Application of a multiple time scale approach gives approximate explicit closed form expressions for the changing population, that compare favorably with those generated from numerical solutions.

MSC:
92D40 Ecology
34D10 Perturbations of ordinary differential equations
37N25 Dynamical systems in biology
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