Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model

Boundary Value Problems

卷:2019

Hongwu Xu¹  Shengmao Fu² 

[1] School of Mathematics and Statistics, Longdong University;

[2] School of Mathematics and Statistics, Northwest Normal University;

关键词: Predator–prey model;    Density-dependent;    Turing instability;    Bifurcation;    Steady state;   

DOI  :  10.1186/s13661-019-1214-0

来源: DOAJ

【 摘 要 】

Abstract In this paper, Turing patterns and steady state bifurcation of a diffusive Beddington–DeAngelis-type predator–prey model with density-dependent death rate for the predator are considered. We first investigate the stability and Turing instability of the unique positive equilibrium point for the model. Then the existence/nonexistence, the local/global structure of nonconstant positive steady state solutions, and the direction of the local bifurcation are established. Our results demonstrate that a Turing instability is induced by the density-dependent death rate under appropriate conditions, and both the general stationary pattern and Turing pattern can be observed as a result of diffusion. Moreover, some specific examples are presented to illustrate our analytical results.

【 授权许可】

Unknown