CNN dynamics represents a broader class than PDEs

M. Gilli, T. Roska, L. O. Chua, P. P. Civalleri

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The relationship between Cellular Nonlinear Networks (CNNs) and Partial Differential Equations (PDEs) is investigated. The equivalence between discrete-space CNN models and continuous-space PDE models is rigorously defined. The key role of space discretization is explained. The problem of the equivalence is split into two subproblems: approximation and topological equivalence, that can be explicitly studied for any CNN model. It is known that each PDE can be approximated by a space difference scheme, i.e. a CNN model, that presents a similar dynamic behavior. It is shown, through several examples, that there exist CNN models that are not equivalent to any PDEs, either because they do not approximate any PDE models, or because they have a qualitatively different dynamic behavior (i.e. they are not topologically equivalent to the PDE that they approximate). This proves that the spatio-temporal CNN dynamics is broader than that described by PDEs.

Original languageEnglish
Pages (from-to)2051-2068
Number of pages18
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
Issue number10
DOIs
Publication statusPublished - Oct 2002

Fingerprint

Nonlinear networks
Network Dynamics
Nonlinear Dynamics
Partial differential equations
Partial differential equation
Network Model
Nonlinear Model
Dynamic Behavior
Equivalence
Topological Equivalence
Class
Difference Scheme
Discretization
Approximation

Keywords

  • Cellular neural networks
  • Cellular nonlinear networks
  • CNN
  • Partial differential equation
  • PDE

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

CNN dynamics represents a broader class than PDEs. / Gilli, M.; Roska, T.; Chua, L. O.; Civalleri, P. P.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 12, No. 10, 10.2002, p. 2051-2068.

Research output: Contribution to journalArticle

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