Complex dynamics in one-dimensional CNNs: Research Articles

Authors:
István Petrás;Marco Gilli
Affiliations:
Analogic and Neural Computing Systems Laboratory, Computer and Automation Research Institute of the Hungarian Academy of Sciences, Kende u.13-17, Budapest 1111, Hungary;Department of Electronics, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
Venue:
International Journal of Circuit Theory and Applications - Special Issue on CNN Technology (Part 1)
Year:
2006

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International Journal of Circuit Theory and Applications

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Abstract

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.