Banerjee, Malay Spatial pattern formation in ratio-dependent model: higher-order stability analysis. (English) Zbl 1216.92058 Math. Med. Biol. 28, No. 2, 111-128 (2011). 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. Cited in 7 Documents 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 Keywords:Hopf bifurcation; Turing instability; stationary pattern; spatiotemporal perturbation Software:PRED_PREY PDFBibTeX XMLCite \textit{M. Banerjee}, Math. Med. Biol. 28, No. 2, 111--128 (2011; Zbl 1216.92058) Full Text: DOI