文章基本信息

标题：Bifurcation, chaos analysis and control in a discrete-time predator–prey system
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作者：Weiyi Liu ; Donghan Cai
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-22
DOI：10.1186/s13662-019-1950-6
出版社：Hindawi Publishing Corporation
摘要：The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory. The existence and stability of fixed points for the model are discussed. It is showed that under certain conditions, the system undergoes a Neimark–Sacker bifurcation when bifurcation parameter passes a critical value, and a closed invariant curve arises from a fixed point. Chaos in the sense of Marotto is also verified by both analytical and numerical methods. Furthermore, to delay or eliminate the bifurcation and chaos phenomena that exist objectively in this system, two control strategies are designed, respectively. Numerical simulations are presented not only to validate analytical results but also to show the complicated dynamical behavior.
关键词：Predator–prey model ; Local stability ; Neimark–Sacker bifurcation ; Marotto’s chaos ; Bifurcation control ; Chaos control