×

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.

MSC:

92D40 Ecology
92C15 Developmental biology, pattern formation
34D20 Stability of solutions to ordinary differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Software:

PRED_PREY
PDFBibTeX XMLCite
Full Text: DOI