The paper considers a class of delayed standard (S) cellular neural networks (CNNs) with non-negative interconnections between distinct neurons and a typical three-segment pwl neuron activation. It is also assumed that such cooperative SCNNs satisfy an irreducibility condition on the interconnection and delayed interconnection matrix. By means of a counterexample it is shown that the solution semiflow associated to such SCNNs in the general case does not satisfy the fundamental property of the omega-limit set dichotomy and is not eventually strongly monotone. The consequences of this result are discussed in the context of the existing methods for addressing convergence of monotone semiflows defined by delayed cooperative dynamical systems.

DI MARCO, M., Forti, M., Grazzini, M., Pancioni, L. (2010). A note on the dichotomy of limit sets for cooperative CNNs with delays. In Proceedings - IEEE International Symposium on Circuits and Systems (pp.2035-2038). IEEE [10.1109/ISCAS.2010.5537175].

A note on the dichotomy of limit sets for cooperative CNNs with delays

DI MARCO, MAURO;FORTI, MAURO;GRAZZINI, MASSIMO;PANCIONI, LUCA
2010-01-01

Abstract

The paper considers a class of delayed standard (S) cellular neural networks (CNNs) with non-negative interconnections between distinct neurons and a typical three-segment pwl neuron activation. It is also assumed that such cooperative SCNNs satisfy an irreducibility condition on the interconnection and delayed interconnection matrix. By means of a counterexample it is shown that the solution semiflow associated to such SCNNs in the general case does not satisfy the fundamental property of the omega-limit set dichotomy and is not eventually strongly monotone. The consequences of this result are discussed in the context of the existing methods for addressing convergence of monotone semiflows defined by delayed cooperative dynamical systems.
2010
9781424453085
DI MARCO, M., Forti, M., Grazzini, M., Pancioni, L. (2010). A note on the dichotomy of limit sets for cooperative CNNs with delays. In Proceedings - IEEE International Symposium on Circuits and Systems (pp.2035-2038). IEEE [10.1109/ISCAS.2010.5537175].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/21346
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