Effect of predator density dependent dispersal of prey on stability of a predator-prey system |
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Authors: | Mchich Rachid Auger Pierre Poggiale Jean-Christophe |
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Institution: | Ecole Nationale de Commerce et de Gestion, Tanger, Morocco. racmchich@yahoo.com |
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Abstract: | This work presents a predator-prey Lotka-Volterra model in a two patch environment. The model is a set of four ordinary differential equations that govern the prey and predator population densities on each patch. Predators disperse with constant migration rates, while prey dispersal is predator density-dependent. When the predator density is large, the dispersal of prey is more likely to occur. We assume that prey and predator dispersal is faster than the local predator-prey interaction on each patch. Thus, we take advantage of two time scales in order to reduce the complete model to a system of two equations governing the total prey and predator densities. The stability analysis of the aggregated model shows that a unique strictly positive equilibrium exists. This equilibrium may be stable or unstable. A Hopf bifurcation may occur, leading the equilibrium to be a centre. If the two patches are similar, the predator density dependent dispersal of prey has a stabilizing effect on the predator-prey system. |
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Keywords: | Predator density dependent prey dispersal Predator-prey system Aggregation of variables Degenerated Hopf bifurcation |
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