On the stability and Hopf bifurcation of a predator-prey model

Advances in Difference Equations

Jianwen Jia¹  Xiaomin Wei¹ 

[1] School of Mathematical and Computer Science, Shanxi Normal University, Linfen, P.R. China

关键词: predator-prey system;    delay;    stage structure;    Hopf bifurcation;   

DOI  :  10.1186/s13662-016-0773-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider a time delay predator-prey model with Holling type-IV functional response and stage-structured for the prey. Our aim is to observe the dynamics of this model under the influence of gestation delay of the predator. We obtain sufficient conditions for the local stability of each of feasible equilibria of the system and the existence of a Hopf bifurcation at the coexistence equilibrium. By using the normal form theory and center manifold theory we also derive some explicit formulae determining the bifurcation direction and the stability of the bifurcated periodic solutions. Finally, numerical simulations are given to explain the theoretical results.

【 授权许可】

CC BY