Bifurcation Analysis of a Ratio-Dependent Holling-Tanner Model with Cross-Diffusion

摘要

In this paper, we investigate a discrete space-time predator-prey model with ratio-dependent function response. The model is given by a coupled map lattice framework, it takes a nonlinear relationship between predator-prey reaction stage and dispersal stage. Through stability analysis and bifurcation analysis, the parameter conditions of Hopf bifurcation is obtained. When adding the cross-diffusion, we obtain the parameter conditions of Turing instability. Numerical simulations verify the theoretical analysis and show a series of spatial patterns.