Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity

Advances in Difference Equations

article

Yang, Ruizhi¹  Ma, Yuxin¹  Zhang, Chiyu¹ 

[1] Department of Mathematics, Northeast Forestry University

关键词: Predator–prey;    Delay;    Stability;    Hopf bifurcation;   

DOI  :  10.1186/s13662-020-03161-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a diffusive predator–prey model with a time delay and prey toxicity. The effect of time delay on the stability of the positive equilibrium is studied by analyzing the eigenvalue spectrum. Delay-induced Hopf bifurcation is also investigated. By utilizing the normal form method and center manifold reduction for partial functional differential equations, the formulas for determining the property of Hopf bifurcation are given.

【 授权许可】

CC BY