Camara, Baba Issa; Aziz-Alaoui, M. A. Turing and Hopf patterns formation in a predator-prey model with Leslie-Gower-type functional response. (English) Zbl 1173.35340 Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 16, No. 4, 479-488 (2009). Summary: We consider a predator-prey system modeled by a reaction-diffusion equation. It incorporates the Holling-type-II and a modified Lesie-Gower functional responses. We focus on spatiotemporal pattern formation. We study how diffusion affects the stability of predator-prey positive equilibrium and derive the conditions for Hopf and Turing bifurcation in the spatial domain. Cited in 2 ReviewsCited in 25 Documents MSC: 35B32 Bifurcations in context of PDEs 35K55 Nonlinear parabolic equations 35K40 Second-order parabolic systems 35K57 Reaction-diffusion equations 92D25 Population dynamics (general) 92C15 Developmental biology, pattern formation Keywords:predator-prey; reaction diffusion; bifurcations; Turing; Hopf; spatiotemporal patterns formation; Hopf and Turing bifurcation PDFBibTeX XMLCite \textit{B. I. Camara} and \textit{M. A. Aziz-Alaoui}, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 16, No. 4, 479--488 (2009; Zbl 1173.35340)