Turing and Hopf patterns formation in a predator-prey model with Leslie-Gower-type functional response. (English) Zbl 1173.35340

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.


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