On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model

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	On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model
	Lin, W ; Ruan, J ; Zhao, WR
	2002-05-01
发表期刊	INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN	0218-1274
卷号	12 期号:5 页码:1129-1139
摘要	We investigate the differences among several definitions of the snap-back-repeller, which is always regarded as an inducement to produce chaos in nonlinear dynamical system. By analyzing the norms in different senses and the illustrative examples, we clarify why a snap-back-repeller in the neighborhood of the fixed point, where all eigenvalues of the corresponding variable Jacobian Matrix are absolutely larger than I in norm, might not imply chaos. Furthermore, we theoretically prove the existence of chaos in a discrete neural networks model in the sense of Marotto with some parameters of the systems entering some regions. And the following numerical simulations and corresponding calculation, as concrete examples, reinforce our theoretical proof.
关键词	snap-back-repeller chaos discrete neural networks
语种	英语
WOS研究方向	Mathematics ; Science & Technology - Other Topics
WOS类目	Mathematics, Interdisciplinary Applications ; Multidisciplinary Sciences
WOS记录号	WOS:000176713500018
出版者	WORLD SCIENTIFIC PUBL CO PTE 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/17164
专题	中国科学院数学与系统科学研究院
通讯作者	Ruan, J
作者单位	1.Fudan Univ, Res Ctr, Dept Math, Shanghai 200433, Peoples R China 2.Fudan Univ, Lab Math Nonlinear Sci, Dept Math, Shanghai 200433, Peoples R China 3.Fudan Univ, Lab Math Nonlinear Sci, Math Inst, Shanghai 200433, Peoples R China 4.Fudan Univ, Res Ctr, Math Inst, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Lin, W,Ruan, J,Zhao, WR. On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2002,12(5):1129-1139.
APA	Lin, W,Ruan, J,&Zhao, WR.(2002).On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,12(5),1129-1139.
MLA	Lin, W,et al."On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model".INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 12.5(2002):1129-1139.