Response of Predator-Prey Systems to Nutrient Enrichment and Proportional Harvesting.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A predator-prey system is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting at a rate proportional to the predator population size are studied. Some theoretical analysis concerning the stability of equilibrium points and the existence of stable limit cycles is included. Three models are examined as examples, and for two of them computer simulations are included to illustrate the changes in qualitative behavior under nutrient enrichment and increase of harvesting effort. The essential difference between this study and our previous work on constant rate harvesting Brauer, Soudack, and Jarosch, 1976 is that here, extinction of predators in finite time is impossible although the predator population may tend to zero as t yields infinity. Also extinction of predators is much less sensitive to changes of harvesting effort than for constant rate harvesting. Author