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Logistic growth with a slowly varying Holling type II harvesting term. (English) Zbl 07261048
Summary: The Holling type II harvesting term has the property that it is small for small population values, but grows monotonically with population growth, eventually saturating, at a constant value for very large populations. We consider here a population evolving according to a logistic rate, but harvested (predated) subject to a Holling type II harvesting term that varies slowly with time, possibly due to slow environmental variation. Application of a multitiming method gives us an approximation to the population at any time in two cases- survival to a slowly varying limit, and extinguishment to zero. The situation where there is a transition from survival to extinction is also analyzed, using a matched expansions approach. A uniformly valid approximate expression for the population, valid for all times is obtained. These results are shown to agree well with the results of numerical calculations.
MSC:
91 Game theory, economics, finance, and other social and behavioral sciences
92 Biology and other natural sciences
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