Effect of predator density dependent dispersal of prey on stability of a predator-prey system

Math Biosci. 2007 Apr;206(2):343-56. doi: 10.1016/j.mbs.2005.11.005. Epub 2006 Feb 7.

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.

MeSH terms

  • Algorithms
  • Animal Migration*
  • Animals
  • Ecosystem
  • Models, Biological*
  • Population Density
  • Population Dynamics
  • Population Growth
  • Predatory Behavior*
  • Spatial Behavior