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Global analysis of a predator-prey model with variable predator search rate
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Paper
Global analysis of a predator-prey model with variable predator search rate
2019
Overview
We consider a modified Rosenzweig-MacArthur predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is presented, and shows that the model exhibits a dichotomy similar to the classical Rosenzweig-MacArthur model: either the coexistence steady state is globally stable; or it is unstable, and then a unique, globally stable limit cycle exists. We discuss the similarities, but also important differences between our model and the Rosenweig-MacArthur model. The main differences are that: 1. The paradox of enrichment which always occurs in the Rosenzweig-MacArthur model, does not always occur here, and 2. Even when the paradox of enrichment occurs, predators can adapt by lowering their search rate, and effectively stabilize the system.
Publisher
Cornell University Library, arXiv.org
Subject
