Cart (Loading....) | Create Account
Close category search window

Convergence of a Class of Cooperative Standard Cellular Neural Network Arrays

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)
Di Marco, M. ; Dipt. di Ing. dell''Inf., Univ. di Siena, Siena, Italy ; Forti, M. ; Grazzini, M. ; Pancioni, L.

This paper considers a nonsymmetric standard (S) cellular neural network (CNN) array with cooperative (nonnegative) interconnections between neurons and a typical three-segment piecewise-linear (PL) neuron activation. The CNN is defined by a one-dimensional cell-linking (irreducible) cloning template with nearest-neighbor interconnections and has periodic boundary conditions. The flow generated by the SCNN is monotone but, due to the squashing effect of the horizontal segments in the PL activations, is not eventually strongly monotone (ESM). A new method for addressing convergence of the cooperative SCNN array is developed, which is based on the two main tools: (1) the concept of a frozen saddle, i.e., an unstable saddle-type equilibrium point (EP) enjoying certain dynamical properties that hold also for an asymptotically stable EP (a sink); (2) the analysis of the order relations satisfied by the sinks and saddle-type EPs. The analysis permits to show a fundamental result according to which any pair of ordered EPs of the SCNN contains at least a sink or a frozen saddle. On this basis it is shown that the flow generated by the SCNN enjoys a LIMIT SET DICHOTOMY and convergence properties analogous to those valid for ESM flows. Such results hold in the case where the SCNN displays either a local diffusion or a global propagation behavior.

Published in:

Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:59 ,  Issue: 4 )

Date of Publication:

April 2012

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.