文献类型：期刊文献

英文题名：Dynamics of a discrete-time predator-prey system

作者：Zhao, Ming[1];Xuan, Zuxing[2];Li, Cuiping[1]

第一作者：Zhao, Ming

通讯作者：Xuan, ZX[1]

机构：[1]Beihang Univ, LMIB, Sch Math & Syst Sci, Beijing 100191, Peoples R China;[2]Beijing Union Univ, Dept Gen Educ, Beijing Key Lab Informat Serv Engn, Beijing 100101, Peoples R China

第一机构：Beihang Univ, LMIB, Sch Math & Syst Sci, Beijing 100191, Peoples R China

通讯机构：[1]corresponding author), Beijing Union Univ, Dept Gen Educ, Beijing Key Lab Informat Serv Engn, Beijing 100101, Peoples R China.|[11417103]北京联合大学北京市信息服务工程重点实验室;[11417]北京联合大学;

年份：2016

卷号：2016

期号：1

外文期刊名：ADVANCES IN DIFFERENCE EQUATIONS

收录：;Scopus(收录号：2-s2.0-84978513792);WOS:【SCI-EXPANDED(收录号:WOS:000379772000001)】；

基金：The authors would like to thank the reviewers and the editor for very helpful suggestions and comments, which led to improvements of our original paper. ZX is the corresponding author and is supported in part by NNSFC (No. 91420202) and the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality (CIT and TCD201504041, IDHT20140508). CL is supported by the National Natural Science Foundation of China (Nos. 61134005, 11272024).

语种：英文

外文关键词：predator-prey system; flip bifurcation; Neimark-Sacker bifurcation; feedback control

摘要：We investigate the dynamics of a discrete-time predator-prey system. Firstly, we give necessary and sufficient conditions of the existence and stability of the fixed points. Secondly, we show that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation by using center manifold theorem and bifurcation theory. Furthermore, we present numerical simulations not only to show the consistence with our theoretical analysis, but also to exhibit the complex but interesting dynamical behaviors, such as the period-6, -11, -16, -18, -20, -21, -24, -27, and -37 orbits, attracting invariant cycles, quasi-periodic orbits, nice chaotic behaviors, which appear and disappear suddenly, coexisting chaotic attractors, etc. These results reveal far richer dynamics of the discrete-time predator-prey system. Finally, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method.