Effect of prey refuge on spatiotemporal dynamics of the reaction-diffusion system

The present investigation deals with the problem of a two-dimensional diffusive predator-prey model incorporating prey refuge. In this investigation, we determine the Turing space in the spatial domain and perform extensive numerical simulation from both the mathematical and the biological points of view in order to study the effect of diffusion coefficients and other momentous parameters of the system in Turing instability. Furthermore, the stability behaviours of the proposed model in the absence of diffusion about the feasible equilibrium points are explored. In particular, the exact Turing domain is delineated in the parameter space. Various spatial patterns in spatial domain through diffusion-driven instability of the present model are depicted and analysed. The results indicate that the effect of prey refuge plays a significant role on the control of pattern formation of the populations. (C) 2014 Elsevier Ltd. All rights reserved.