Predator-prey dynamics with Allee effect in prey refuge

Advances in Difference Equations

Longxing Qi¹  Lijuan Gan¹  Sakhone Sysavathdy¹  Meng Xue¹ 

[1] School of Mathematical Sciences, Anhui University, Hefei, P.R. China

关键词: predator-prey model;    refuge;    fast-slow system;    Allee effect;    Hopf bifurcation;   

DOI  :  10.1186/s13662-015-0673-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we establish a predator-prey model with a refuge and an open habitat for prey. The Allee effect in a prey refuge and the environment carrying capacity of prey are considered. According to biology of prey and predator, fast and slow time scales are considered in some parameters. Based on two different time scales, the system is divided into a fast system and a slow system. Applying the singular perturbation techniques, we analyze the dynamics on the slow system. The stability analyses are performed, and the Hopf bifurcation occurs when the environment carrying capacity of prey is greater than a critical value. This value is an increasing function of the Allee effect. By calculating the first Lyapunov coefficient, the stable periodical oscillation is shown. It is shown that the carrying capacity of prey and the Allee effect of prey in the refuge can influence biological environment.

【 授权许可】

CC BY