Approximation of attractors of nonautonomous dynamical systems

Bernd Aulbach; Martin Rasmussen; Stefan Siegmund

doi:10.3934/dcdsb.2005.5.215

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2005, Volume 5, Issue 2: 215-238. Doi: 10.3934/dcdsb.2005.5.215

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Approximation of attractors of nonautonomous dynamical systems

1.
Department of Mathematics, University of Augsburg, D-86135 Augsburg
2.
Department of Mathematics, University of Frankfurt, D-60325 Frankfurt

Received: December 2003

Revised: July 2004

Published: May 2008

Abstract / Introduction Related Papers Cited by

Abstract

This paper is devoted to the numerical approximation of attractors. For general nonautonomous dynamical systems we first introduce a new type of attractor which includes some classes of noncompact attractors such as unbounded unstable manifolds. We then adapt two cell mapping algorithms to the nonautonomous setting and use the computer program GAIO for the analysis of an explicit example, a two-dimensional system of nonautonomous difference equations. Finally we present numerical data which indicate a bifurcation of nonautonomous attractors in the Duffing-van der Pol oscillator.

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Mathematics Subject Classification: 34C30, 34D45, 37B55, 37G35, 39A10, 65L20.

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