Bifurcation and chaos in a discrete genetic toggle switch system

doi:10.1016/j.chaos.2004.05.027

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	Bifurcation and chaos in a discrete genetic toggle switch system
	Jing, ZJ ; Huang, JC
	2005-02-01
发表期刊	CHAOS SOLITONS & FRACTALS
ISSN	0960-0779
卷号	23 期号:3 页码:887-908
摘要	A discrete genetic toggle switch system obtained by Euler method is first investigated. The conditions of existence for fold bifurcation and flip bifurcation are derived by using center manifold theorem and bifurcation theory. The numerical simulations, including bifurcation diagrams, phase portraits, and computation of Lyapunov exponents, not only show the consistence with the theoretical analysis but also exhibit the rich and complex dynamical behavior. We show the period 3 to 13 windows in different chaotic regions, period-doubling bifurcation or inverse period-doubling bifurcation from period-2 to 12 orbits leading to chaos, different kind of interior crisis and boundary crisis, intermittency behavior, chaotic set, chaotic non-attracting set, coexistence of period points with invariant cycles, and so on. The influence of the amplitude and frequency of excitable forcing on the system are also first considered by using numerical simulation. A different type of quasiperiodic orbits, jumping behaviors of quasiperiodic set from one set to another set, and the processes from quasiperiodic orbits to strange non-chaotic attractor are found. (C) 2004 Elsevier Ltd. All rights reserved.
DOI	10.1016/j.chaos.2004.05.027
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:000224600200020
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/1199
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, Inst Math, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China
推荐引用方式 GB/T 7714	Jing, ZJ,Huang, JC. Bifurcation and chaos in a discrete genetic toggle switch system[J]. CHAOS SOLITONS & FRACTALS,2005,23(3):887-908.
APA	Jing, ZJ,&Huang, JC.(2005).Bifurcation and chaos in a discrete genetic toggle switch system.CHAOS SOLITONS & FRACTALS,23(3),887-908.
MLA	Jing, ZJ,et al."Bifurcation and chaos in a discrete genetic toggle switch system".CHAOS SOLITONS & FRACTALS 23.3(2005):887-908.