On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks

doi:10.1109/TNN.2010.2102048

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	On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks
	Lu, Wenlian 1,2; Wang, Lili 3; Chen, Tianping 4
刊名	IEEE TRANSACTIONS ON NEURAL NETWORKS
	2011-03
卷号	22 期号:3 页码:381-394
关键词	Attracting basin cellular neural networks complete stability multistability
ISSN号	1045-9227
DOI	10.1109/TNN.2010.2102048
英文摘要	In this paper, we study the distribution of attraction basins of multiple equilibrium points of cellular neural networks (CNNs). Under several conditions, the boundaries of the attracting basins of the stable equilibria of a completely stable CNN system are composed of the closures of the stable manifolds of unstable equilibria of (n - 1) dimensions. As demonstrations of this idea, under the conditions proposed in the literature which depicts stable and unstable equilibria, we identify the attraction basin of each stable equilibrium of which the boundary is composed of the stable manifolds of the unstable equilibria precisely. We also investigate the attracting basins of a simple class of symmetric 1-D CNNs via identifying the unstable equilibria of which the stable manifold is (n - 1) dimensional and the completely stable asymmetric CNNs with stable equilibria less than 2(n).
WOS研究方向	Computer Science ; Engineering
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000287862500005
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/2290]
专题	上海财经大学
通讯作者	Lu, Wenlian
作者单位	1.Fudan Univ, Ctr Computat Syst Biol, Shanghai 200433, Peoples R China; 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China; 3.Shanghai Univ Finance & Econ, Dept Appl Math, Shanghai 200433, Peoples R China; 4.Fudan Univ, Sch Math Sci, Chinese Minist Educ, Key Lab Nonlinear Sci, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Lu, Wenlian,Wang, Lili,Chen, Tianping. On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks[J]. IEEE TRANSACTIONS ON NEURAL NETWORKS,2011,22(3):381-394.
APA	Lu, Wenlian,Wang, Lili,&Chen, Tianping.(2011).On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks.IEEE TRANSACTIONS ON NEURAL NETWORKS,22(3),381-394.
MLA	Lu, Wenlian,et al."On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks".IEEE TRANSACTIONS ON NEURAL NETWORKS 22.3(2011):381-394.