Direct exponential ordering for neutral compartmental systems with  non-autonomous $\mathbf{D}$-operator

Rafael Obaya; Víctor M. Villarragut

doi:10.3934/dcdsb.2013.18.185

Article Contents

2013, Volume 18, Issue 1: 185-207. Doi: 10.3934/dcdsb.2013.18.185

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Direct exponential ordering for neutral compartmental systems with non-autonomous $\mathbf{D}$-operator

Rafael Obaya^1, and
Víctor M. Villarragut^2,

1.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales and member of IMUVA, Instituto de Matemáticas, Universidad de Valladolid, 47011 Valladolid
2.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, Universidad de Valladolid, 47011 Valladolid

Received: April 30, 2012

Revised: June 30, 2012

Published: December 2012

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Abstract

We study closed compartmental systems described by neutral functional differential equations with non-autonomous stable $D$-operator which are monotone for the direct exponential ordering. Under some appropriate conditions on the induced semiflow including uniform stability for the exponential order and the differentiability of the $D$-operator along the base flow, we establish the 1-covering property of omega-limit sets, in order to describe the long-term behavior of the trajectories.

Keywords:

Non-autonomous dynamical systems,
monotone skew-product semiflows,
neutral functional differential equations,
infinite delay,
compartmental systems.

Mathematics Subject Classification: 37B55, 34K40, 34K14.

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