Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey

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Abstract

The dynamics of a reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. Nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity.

MSC

35K57
35B36
35B32
92D40

Keywords

Reaction–diffusion system
Predator–prey
Bifurcation
Strong Allee effect
Spatiotemporal patterns

Cited by (0)

This research is partially supported by the National Natural Science Foundation of China (Nos. 11031002, 11071051), National Science Foundation of US (DMS-1022648).