Coexistence Region and Global Dynamics of a Harvested Predator-Prey System
Guoren Dai, Moxun Tang
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Source: Crossref
Published: Feb 1, 1998
DOI: 10.1137/s0036139994275799
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The study of populational dynamics with harvesting is related to the optimal management of renewable resources. In this paper we consider a predator-prey model in which two ecologically interacting species are harvested independently with constant rates. The main purpose of the present work is to offer a complete mathematical analysis for the model and to describe some of the significant qualitative results that may be expected to arise from the interplay of biological forces. Our study shows that the maximum safe harvest may be far less than what would be assumed from a local analysis for the equilibria. It is also proved that the harvested predator-prey system may exhibit very complicated dynamics such as a spontaneous appearance of a homoclinic orbit and multiple limit cycles.
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