© Hindawi Publishing Corp. DIFFUSIVE INSTABILITY IN A PREY-PREDATOR SYSTEM WITH TIME-DEPENDENT DIFFUSIVITY

Abstract

An ecological model for prey-predator planktonic species has been considered, in which the growth of prey has been assumed to follow a Holling type II function. The model consists of two reaction-diffusion equations and we extend it to timevarying diffusivity for plankton population. A comparative study of local stability in case of constant diffusivity and time varying diffusivity has been performed. It has been found that the system would be more stable with time varying diffusivity depending upon the values of system parameter. 2000 Mathematics Subject Classification: 37G15. 1. Introduction. In 1952, Turing [10] proposed a diffusion-reaction theory of morphogenesis on the basis of well-known laws of physical chemistry. This concept has been extended to develop the theory of biological pattern formation. In an ecological context, Segel and Jackson [8] were the first to apply Turing’s model to predator-prey system. Since then, diffusive instabilit