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

Sylvia Novo; Rafael Obaya; Ana M. Sanz

doi:10.3934/dcds.2007.18.517

Article Contents

2007, Volume 18, Issue 2&3: 517-536. Doi: 10.3934/dcds.2007.18.517

This issue Previous Article Continuous dependence of attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems Next Article Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems

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
2.
Universidad de Valladolid, Departamento de Análisis Matemático y Didáctica de la Matemática, Prado de la Magdalena s/n, 47005 Valladolid

Received: February 28, 2006

Revised: April 30, 2006

Published: May 2007

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Abstract

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.

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Mathematics Subject Classification: 37B55, 37C65, 34K14, 92B20.

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