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February & March  2007, 18(2&3): 517-536. doi: 10.3934/dcds.2007.18.517

Exponential stability in non-autonomous delayed equations with applications to neural networks

1. 

Universidad de Valladolid, Departamento de Matemática Aplicada, ETSII, Paseo del Cauce s/n, 47011 Valladolid, Spain, Spain

2. 

Universidad de Valladolid, Departamento de Análisis Matemático y Didáctica de la Matemática, Prado de la Magdalena s/n, 47005 Valladolid, Spain

Received  March 2006 Revised  May 2006 Published  March 2007

We consider the skew-product semiflow induced by a family of finite-delay functional differential equations and we characterize the exponential stability of its minimal subsets. In the case of non-autonomous systems modelling delayed cellular neural networks, the existence of a global exponentially attracting solution is deduced from the uniform asymptotical stability of the null solution of an associated non-autonomous linear system.
Citation: Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in non-autonomous delayed equations with applications to neural networks. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 517-536. doi: 10.3934/dcds.2007.18.517
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