Density dependent harvesting of a logistic population in a slowly varying environment

Tatjana Grozdanovski, John J Shepherd, Andrew J Stacey

Abstract


We apply a multiscale method to construct general analytic approximations for the solution of a harvested logistic system, where the system parameters vary slowly in time. Such approximations are a useful alternative to numerical solutions and are applicable to a range of parameter values. We consider two situations: subcritical harvesting, where the population survives; and supercritical harvesting, where it is driven to extinction. These approximations give excellent agreement with the numerical solutions of test cases.

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Keywords


multi-scaling; harvesting; slow variation

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DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2271



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