Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting

An appropriate mathematical structure to describe the population dynamics is given by the partial differential equations of reaction-diffusion type. The spatiotemporal dynamics and bifurcations of a ratio-dependent Holling type II predator-prey model system with both the effect of linear prey harvesting and constant proportion of prey refuge are investigated. The existence of all ecologically feasible equilibria for the non-spatial model is determined, and the dynamical classifications of these equilibria are developed. The model system representing initial boundary value problem under study is subjected to zero flux boundary conditions. The conditions of diffusion-driven instability and the Turing bifurcation region in two parameter space are explored. The consequences of spatial pattern analysis in two-dimensional domain by means of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e. spotted or stripe-like patterns or coexistence of both the patterns or labyrinthine patterns and so on. The results around the unique interior feasible equilibrium solution indicate that the effect of refuge and harvesting plays a significant role on the control of spatial pattern formation of the species. Finally, the paper ends with a comprehensive discussion of biological implications of our findings.