Paper Info
Title
On attracting basins of multiple equilibria of a class of cellular neural networks.
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 2(n).
Year
DOI
Venue
2011
10.1109/TNN.2010.2102048
IEEE Transactions on Neural Networks
Keywords
Field
DocType
multiple equilibria,unstable equilibrium,stable cnn system,attracting basin,stable asymmetric cnns,attracting basins,complete stability,multistability,stable manifold,cellular neural networks,cnn,cellular neural network,multiple equilibrium point,cellular neural nets,attraction basin,stable equilibrium,simple class,1-d cnns,artificial neural network,artificial neural networks,trajectory,manifolds,asymptotic stability,artificial intelligence,indexes,nonlinear dynamics,indexation,algorithms
Stable manifold,Equilibrium point,Exponential stability,Artificial intelligence,Multistability,Manifold,Boundary value problem,Mathematical optimization,Pattern recognition,Pure mathematics,Cellular neural network,Mathematics,Structural basin
Journal
Volume
Issue
ISSN
22
3
1941-0093
Citations 
PageRank 
References 
27
1.23
18
Authors
3
Name
Order
Citations
PageRank
Wenlian Lu1133193.47
Lili Wang226913.90
Tianping Chen33095250.77