Dynamics in a discrete-time predator-prey system with Allee effect

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	Dynamics in a discrete-time predator-prey system with Allee effect
其他题名	Dynamics in a Discrete-time Predator-prey System with Allee Effect
	Chen Xianwei 1; Fu Xiangling 2; Jing Zhujun 1
	2013
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	29 期号:1 页码:143-164
摘要	In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value). Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.
其他摘要	In this paper, dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail. Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory, and then further illustrated by numerical simulations. Chaos in the sense of Marotto is proved by both analytical and numerical methods. Numerical simulations included bifurcation diagrams, Lyapunov exponents, phase portraits, fractal dimensions display new and rich dynamical behavior. More specifically, apart from stable dynamics, this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it. The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior. The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value). Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the discrete-time predator-prey with Allee effect is given.
关键词	POPULATION-DYNAMICS CHAOS MODEL Predator-prey System Allee effect flip bifurcation Hopf bifurcation Marotto's chaos transient chaos invariant circle periodic window
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:4787296
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52685
专题	中国科学院数学与系统科学研究院
作者单位	1.湖南师范大学 2.湖南大学 3.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Chen Xianwei,Fu Xiangling,Jing Zhujun. Dynamics in a discrete-time predator-prey system with Allee effect[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2013,29(1):143-164.
APA	Chen Xianwei,Fu Xiangling,&Jing Zhujun.(2013).Dynamics in a discrete-time predator-prey system with Allee effect.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,29(1),143-164.
MLA	Chen Xianwei,et al."Dynamics in a discrete-time predator-prey system with Allee effect".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 29.1(2013):143-164.