Spatiotemporal patterns in a diffusive predator-prey model with prey social behavior. (English) Zbl 1459.35244
Summary: Our aim in this paper is to investigate the behavior of pattern formation for a predator-prey model with social behavior and spatial diffusion. Firstly, we give some solution behavior where the non-existence of a non-constant steady state solution has been proved for some values of the diffusion coefficients. On the other hand, by using the Leray-Schauder degree theory the existence of the non-constant steady-state solution has been proved under a suitable conditions on the diffusion coefficients.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D25 | Population dynamics (general) |
| 35B32 | Bifurcations in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
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