title: Effect of predator density dependent dispersal of prey on stability of a predator-prey system.
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.
authors.affiliation: Ecole Nationale de Commerce et de Gestion, Tanger, Morocco. racmchich@yahoo.com
authors.forename: Rachid
authors.initials: R
authors.lastname: Mchich
authors.forename: Pierre
authors.initials: P
authors.lastname: Auger
authors.forename: Jean-Christophe
authors.initials: JC
authors.lastname: Poggiale
mesh_terms: D000465:Algorithms; D025041:Animal Migration; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth; D011235:Predatory Behavior; D013037:Spatial Behavior