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

Content Provider	IEEE Xplore Digital Library
Author	Wenlian Lu Lili Wang Tianping Chen
Copyright Year	1990
Abstract	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 2ⁿ.
Sponsorship	IEEE Computational Intelligence Society
Page Count	14
File Size	883363
Starting Page	381
Ending Page	394
File Format	PDF
ISSN	10459227
Volume Number	22
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-03-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Manifolds Eigenvalues and eigenfunctions Indexes Trajectory Artificial neural networks Asymptotic stability Neurons multistability Attracting basin cellular neural networks complete stability
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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