Continuousseparation for monotone skew-productsemiflows: From theoretical to numerical results

Juan A. Calzada; Rafael Obaya; Ana M. Sanz

doi:10.3934/dcdsb.2015.20.915

Article Contents

2015, Volume 20, Issue 3: 915-944. Doi: 10.3934/dcdsb.2015.20.915

This issue Previous Article Remarks on linear-quadratic dissipative control systems Next Article Belitskii--Lyubich conjecture for $C$-analytic dynamical systems

Continuous separation for monotone skew-product semiflows: From theoretical to numerical results

1.
Departamento de Matemática Aplicada, E. Ingenierías Industriales, Universidad de Valladolid, 47011 Valladolid
2.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 47011 Valladolid
3.
Departamento de Didáctica de las Ciencias Experimentales, Sociales y de la Matemática, Facultad de Educación and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 34004 Palencia

Received: September 2013

Revised: May 2014

Published: May 2015

Abstract / Introduction Related Papers Cited by

Abstract

This paper investigates relevant dynamical properties of nonautonomous linear cooperative families of ODEs and FDEs based on the existence of a continuous separation. It provides numerical algorithms for the computation of the dominant one-dimensional subbundle of the continuous separation and the upper Lyapunov exponent of the semiflow. The extension of the theory to general linear cooperative families of ODEs and FDEs without strong monotonicity is also given. Finally these methods and results are applied in the study of nonlinear families of neural networks of Hopfield type with sigmoidal activation function.

Keywords:

Monotone skew-product semiflows,
uniform persistence,
continuous separation,
numerical methods for Lyapunov exponents,
neural networks.

Mathematics Subject Classification: 37C60, 37C65, 37M25, 37B05.

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