Dynamical behavior in linearly coupled Oregonators

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	Dynamical behavior in linearly coupled Oregonators
	Zhou, TS; Zhang, SC
	2001-05-01
发表期刊	PHYSICA D
ISSN	0167-2789
卷号	151 期号:2-4 页码:199-216
摘要	Tyson [Ann. NY Acad. Sci. 316 (1979) 279] conjectured that the stable homogeneous positive steady state may coexist with stable echo wave (meaning anti-phase wave) in linearly coupled Oregonators land thus gave a conjecture on the bifurcation diagram of this system). In this paper, we rigorously prove stability of the in-phase wave and existence of the anti-phase wave. Our proof procedure actually gives a general method (or line) to deal with the analogous problem. For instance, to prove stability of the in-phase wave, following our line one may decompose the corresponding variational equations (a four-dimensional system) into two independent planar systems; also for instance, existence of the anti-phase wave can be concluded as existence and uniqueness of limit cycle of the associate oscillator. In addition, according to parameter regimes of existence of the anti-phase wave and the stable homogeneous positive steady state, we give their coexistence regime and specify it, and in particular give the regime of the coupled coefficient. The specified results show that the theoretical results are in good accord with Tyson's numerical results. (C) 2001 Elsevier Science B.V. All rights reserved.
关键词	coupled oregonators single oscillator associate oscillator in-phase wave echo wave normal form
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000168775400006
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/16575
专题	中国科学院数学与系统科学研究院
通讯作者	Zhou, TS
作者单位	Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhou, TS,Zhang, SC. Dynamical behavior in linearly coupled Oregonators[J]. PHYSICA D,2001,151(2-4):199-216.
APA	Zhou, TS,&Zhang, SC.(2001).Dynamical behavior in linearly coupled Oregonators.PHYSICA D,151(2-4),199-216.
MLA	Zhou, TS,et al."Dynamical behavior in linearly coupled Oregonators".PHYSICA D 151.2-4(2001):199-216.