Paper Info
Title
A study on semiflows generated by cooperative full-range CNNs
Abstract
The paper considers the full-range (FR) model of cellular neural networks (CNNs) characterized by ideal hard-limiter nonlinearities with two vertical segments in the current–voltage characteristic. It is shown that when the FRCNNs are cooperative, i.e., there are excitatory interconnections between distinct neurons, the generated solution semiflow is monotone and that monotonicity implies some fundamental restrictions on the geometry of omega-limit sets. The result on monotonicity is a generalization to the class of differential inclusions describing the dynamics of FRCNNs of a classic result due to Kamke for cooperative ordinary differential equations. The paper also points out difficulties to use the standard theory of eventually strongly monotone (ESM) semiflows for addressing convergence of FRCNNs. By means of counterexamples, it is shown that, even assuming the irreducibility of the interconnections, the semiflow generated by a cooperative FRCNN is not ESM; furthermore, also the limit set dichotomy can be violated. Copyright © 2012 John Wiley & Sons, Ltd.
Year
DOI
Venue
2012
10.1002/cta.1797
I. J. Circuit Theory and Applications
Keywords
Field
DocType
distinct neuron,cooperative frcnn,fundamental restriction,cellular neural network,solution semiflow,differential inclusion,cooperative ordinary differential equation,classic result,john wiley,excitatory interconnection,cooperative full-range cnns,differential inclusions,cellular neural networks
Differential inclusion,Monotonic function,Discrete mathematics,Ordinary differential equation,Control theory,Irreducibility,Pure mathematics,Strongly monotone,Cellular neural network,Monotone polygon,Limit set,Mathematics
Journal
Volume
Issue
ISSN
40
12
0098-9886
Citations 
PageRank 
References 
3
0.38
13
Authors
5
Name
Order
Citations
PageRank
Mauro Di Marco120518.38
Mauro Forti239836.80
Massimo Grazzini313111.01
Paolo Nistri421233.80
Luca Pancioni520717.58