Dynamics of a Delayed Predator-prey System with Stage Structure for Predator and Prey  

作　　者：Liu Juan Zhang Zi-zhen Li Yong 

机构地区：[1]Department of Mathematics and Physics, Bengbu College [2]School of Management Science and Engineering, Anhui University of Finance and Economics

出　　处：《Communications in Mathematical Research》2015年第4期298-310,共13页数学研究通讯（英文版）

基　　金：The NSF(KJ2013A003,KJ2013B137)of the Higher Education Institutions of Anhui Province

摘　　要：In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally~ numerical simulations are presented to support the theoreticM analysis.In this paper, a predator-prey system with two discrete delays and stage structure for both the predator and the prey is investigated. The dynamical behaviors such as local stability and local Hopf bifurcation are analyzed by regarding the possible combinations of the two delays as bifurcating parameter. Some explicit formulae determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and the center manifold theory. Finally~ numerical simulations are presented to support the theoreticM analysis.

关 键 词：time delay STAGE-STRUCTURE Hopf bifurcation stability periodic solution 

分 类 号：O175[理学—数学]