Dynamics in a diffusive predator-prey system with double Allee effect and modified Leslie-Gower scheme. (English) Zbl 1491.35024
Summary: In this paper, we investigate a diffusive modified Leslie-Gower predator-prey system with double Allee effect on prey. The global existence, uniqueness and a priori bound of positive solutions are determined. The existence and local stability of constant steady-state solutions are analyzed. Next, we induce the nonexistence of nonconstant positive steady-state solutions, which indicates the effect of large diffusivity. Furthermore, we discuss the steady-state bifurcation and the existence of nonconstant positive steady-state solutions by the bifurcation theory. In addition, Hopf bifurcations of the spatially homogeneous and inhomogeneous periodic orbits are studied. Finally, we make some numerical simulations to validate and complement the theoretical analysis. Our results demonstrate that the dynamics of the system with double Allee effect and modified Leslie-Gower scheme are richer and more complex.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B09 | Positive solutions to PDEs |
| 35B35 | Stability in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
Keywords:
predator-prey system; double Allee effect; stability; numerical simulations; steady-state bifurcation; Hopf bifurcationsReferences:
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