文章基本信息

标题：Complex dynamic behavior of a discrete-time predator-prey system of Holling-III type
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作者：Zhimin He ; Bo Li
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：180
DOI：10.1186/1687-1847-2014-180
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-III type in the closed first quadrant R + 2 . Firstly, the existence and stability of fixed points of the system is discussed. Secondly, it is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R + 2 by using bifurcation theory. Finally, numerical simulations including bifurcation diagrams, phase portraits, and maximum Lyapunov exponents are presented not only to explain our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-6, -7, -9, -15, -16, -22, -23, -32, -35 orbits, a cascade of period-doubling bifurcations in period-2, -4, -8, -16 orbits, quasi-periodic orbits, and chaotic sets. MSC: 37G05, 37G35, 39A28, 39A33.
关键词：discrete dynamical system ; predator-prey system ; chaos ; Lyapunov exponent ; stability ; period-doubling ; flip bifurcation ; Neimark-Sacker bifurcation