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Spatial pattern formation in ratio-dependent model: higher-order stability analysis. (English) Zbl 1216.92058
Summary: The article presents a study of spatiotemporal pattern formation in a Holling-Tanner prey-predator model with ratio-dependent functional response. Conditions for Turing bifurcations are obtained and different spatially inhomogeneous stationary patterns exhibited by the model system are presented. The reported patterns are the outcome of numerical simulation. The conditions for instability of inhomogeneous spatiotemporal perturbations around temporal steady states beyond the linear regime fall out from the analysis of higher-order perturbation terms. The analytical findings are validated with numerical simulation results.

92C15Developmental biology, pattern formation
34D20Stability of ODE
65C20Models (numerical methods)
35Q92PDEs in connection with biology and other natural sciences
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