Spatial pattern formation in ratio-dependent model: higher-order stability analysis

Abstract

The article presents a study of the spatiotemporal pattern formation in a Holling–Tanner prey–predator model with ratio-dependent functional response. Conditions for Turing bifurcation are obtained and different spatially inhomogeneous stationary patterns exhibited by the model system are presented. Then, reported patterns are the outcome of numerical simulation. The conditions for instability of inhomogeneous spatiotemporal perturbation around temporal steady state beyond the linear regime fall out from the analysis of higher-order perturbation terms. The analytical findings are validated with the numerical simulation results.

stability, Hopf bifurcation, Turing instability, stationary pattern, spatiotemporal perturbation