Global asymptotic stability for neural network models with distributed delays

Authors:
José J. Oliveira
Affiliations:
Departamento de Matemática and CMAT, Escola de Ciências, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 10
Cited 5

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Abstract

In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the non-delayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well-known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.