Pattern formation of a diffusive predator–prey model with strong Allee effect and nonconstant death rate

Shao-Wen Yao, Zhan-Ping Ma and Zhi-Bo Cheng

Physica A: Statistical Mechanics and its Applications, 2019, vol. 527, issue C

Abstract: This paper is concerned with the pattern formation of a diffusive predator–prey model with strong Allee effect in the prey population and nonconstant death rate for the predator. The necessary and sufficient conditions of Turing instability are explicitly obtained. By regarding the diffusion coefficient d2 of the predator as bifurcation parameter, we demonstrate that at the critical value of the bifurcation parameter d2 a Turing bifurcation occurs (i.e. a pattern arises). The conditions for the stability of the pattern are also derived in detail. Our results show that strong Allee effect in our model plays a crucial role in the formation of stationary pattern, which is a strong contrast to the case without strong Allee effect.

Keywords: Diffusive predator–prey model; Strong Allee effect; Nonconstant death rate; Turing bifurcation; Stability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:527:y:2019:i:c:s0378437119307964

DOI: 10.1016/j.physa.2019.121350

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