It is known that symmetric cellular neural networks (CNNs) are completely stable, i.e., each trajectory converges towards some equilibrium point. The paper addresses the issue of the loss of CNN complete stability caused by errors in the implementation of the nominal symmetric interconnections. The main result is a structural condition which implies the existence of stable limit cycles generated via Hopf bifurcations, even for arbitrarily small perturbations of the nominal interconnections. Furthermore, analytic results providing an approximate relationship between the limit cycle features and the fundamental CNN parameters are presented.
DI MARCO, M., Forti, M., Tesi, A. (2002). A study on limit cycles in nearly symmetric cellular neural networks. In Proceedings of the 2002 7th IEEE International Workshop on Cellular Neural Networks and Their Applications (CNNA 2002) (pp.41-46). New York : IEEE [10.1109/CNNA.2002.1035033].
A study on limit cycles in nearly symmetric cellular neural networks
DI MARCO, MAURO;FORTI, MAURO;
2002-01-01
Abstract
It is known that symmetric cellular neural networks (CNNs) are completely stable, i.e., each trajectory converges towards some equilibrium point. The paper addresses the issue of the loss of CNN complete stability caused by errors in the implementation of the nominal symmetric interconnections. The main result is a structural condition which implies the existence of stable limit cycles generated via Hopf bifurcations, even for arbitrarily small perturbations of the nominal interconnections. Furthermore, analytic results providing an approximate relationship between the limit cycle features and the fundamental CNN parameters are presented.
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https://hdl.handle.net/11365/24620