Stability and Hopf bifurcation for a ratio-dependent predator-prey system with stage structure and time delay

Advances in Difference Equations

Guanghui Feng¹  Lingshu Wang² 

[1] Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, P.R. China;School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, P.R. China

关键词: predator-prey system;    stage structure;    time delay;    stability;    Hopf bifurcation;    34K18;    34K20;    34K60;    92D25;   

DOI  :  10.1186/s13662-015-0548-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A ratio-dependent predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of the predator-extinction equilibrium and the coexistence equilibrium of the system are discussed, respectively. Further, the existence of Hopf bifurcation at the coexistence equilibrium is also studied. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the analytical results.

【 授权许可】

CC BY