Spatiotemporal Dynamics of a Diffusive Leslie-Gower Predator-Prey Model with Ratio-Dependent Functional Response

This paper is devoted to the study of spatiotemporal dynamics of a diffusive Leslie-Gower predator-prey system with ratio-dependent Holling type III functional response under homogeneous Neumann boundary conditions. It is shown that the model exhibits spatial patterns via Turing (diffusion-driven) instability and temporal patterns via Hopf bifurcation. Moreover, the existence of spatiotemporal patterns is established via Turing-Hopf bifurcation at the degenerate points where the Turing instability curve and the Hopf bifurcation curve intersect. Various numerical simulations are also presented to illustrate the theoretical results.