Bifurcation and chaos in discrete-time predator-prey system

doi:10.1016/j.chaos.2005.03.040

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	Bifurcation and chaos in discrete-time predator-prey system
	Jing, ZJ ; Yang, JP
	2006
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	27 期号:1 页码:259-277
摘要	The discrete-time predator-prey system obtained by Euler method is investigated. The conditions of existence for flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory. And numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including period-3,5,6,7,8,9,10,12,18,20,22,30,39-orbits in different chaotic regions, attracting invariant circle, period-doubling bifurcation from period-10 leading to chaos, inverse period-doubling bifurcation from period-5 leading to chaos, interior crisis and boundary crisis, intermittency mechanic, onset of chaos suddenly and sudden disappearance of the chaotic dynamics, attracting chaotic set, and non-attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The computations of Lyapunov exponents confirm the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology. (c) 2005 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.chaos.2005.03.040
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Interdisciplinary Applications ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000232094700028
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3453
专题	中国科学院数学与系统科学研究院
通讯作者	Jing, ZJ
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Jing, ZJ,Yang, JP. Bifurcation and chaos in discrete-time predator-prey system[J]. CHAOS SOLITONS & FRACTALS,2006,27(1):259-277.
APA	Jing, ZJ,&Yang, JP.(2006).Bifurcation and chaos in discrete-time predator-prey system.CHAOS SOLITONS & FRACTALS,27(1),259-277.
MLA	Jing, ZJ,et al."Bifurcation and chaos in discrete-time predator-prey system".CHAOS SOLITONS & FRACTALS 27.1(2006):259-277.