Asymptotic behaviour of a non-autonomous Lorenz-84 system

María Anguiano; Tomás Caraballo

doi:10.3934/dcds.2014.34.3901

Article Contents

2014, Volume 34, Issue 10: 3901-3920. Doi: 10.3934/dcds.2014.34.3901

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Asymptotic behaviour of a non-autonomous Lorenz-84 system

María Anguiano^1, and
Tomás Caraballo^2,

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080-Sevilla
2.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla

Received: February 28, 2013

Revised: March 31, 2013

Published: September 2014

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Abstract

The so called Lorenz-84 model has been used in climatological studies, for example by coupling it with a low-dimensional model for ocean dynamics. The behaviour of this model has been studied extensively since its introduction by Lorenz in 1984. In this paper we study the asymptotic behaviour of a non-autonomous Lorenz-84 version with several types of non-autonomous features. We prove the existence of pullback and uniform attractors for the process associated to this model. In particular we consider that the non-autonomous forcing terms are more general than almost periodic. Finally, we estimate the Hausdorff dimension of the pullback attractor. We illustrate some examples of pullback attractors by numerical simulations.

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Mathematics Subject Classification: 37B55, 35B41, 37L30.

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