Hopf Bifurcation and Stability Analysis for a Predator-prey Model with Time-delay  

具有时滞的食饵捕食系统的Hopf分支及分支周期解的稳定性（英文）

作　　者：陈红兵 

机构地区：[1]School of Mathematics and Statistics, Tianshui Normal University

出　　处：《Chinese Quarterly Journal of Mathematics》2015年第1期93-106,共14页数学季刊（英文版）

基　　金：Supported by the the NSF of Gansu Province(096RJZE106)

摘　　要：In this paper, a predator-prey model of three species is investigated, the necessary and sucient of the stable equilibrium point for this model is studied. Further, by introduc-ing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.

关 键 词：Hopf bifurcation stability time delay predator-prey system periodic solution 

分 类 号：O175.17[理学—数学]