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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Asymptotic behaviour of a non-autonomous Lorenz-84 system

Pages: 3901 - 3920, Volume 34, Issue 10, October 2014      doi:10.3934/dcds.2014.34.3901

 
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María Anguiano - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080-Sevilla, Spain (email)
Tomás Caraballo - Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla, Spain (email)

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.

Keywords:  Lorenz system, non-autonomous equation, pullback attractor, uniform attractor, Hausdorff dimensionn.
Mathematics Subject Classification:  37B55, 35B41, 37L30.

Received: March 2013;      Revised: April 2013;      Available Online: April 2014.

 References