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Complex dynamics in one‐dimensional CNNs
Author(s) -
Petrás István,
Gilli Marco
Publication year - 2006
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.340
Subject(s) - attractor , bifurcation , chaotic , cellular neural network , instability , boundary (topology) , equilibrium point , sign (mathematics) , diagonal , dynamics (music) , multistability , statistical physics , mathematics , stability (learning theory) , computer science , mathematical analysis , physics , artificial neural network , artificial intelligence , nonlinear system , geometry , mechanics , quantum mechanics , machine learning , acoustics , differential equation
The effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one‐dimensional template CNNs are considered. It is shown that if the off‐diagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very rich and complex dynamic behaviour. In particular, they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractors and to the coexistence of several attractors. Then the influence of the number of cells on the global dynamics is studied, with particular reference to the occurrence of hyperchaotic behaviour. Copyright © 2006 John Wiley & Sons, Ltd.