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May  2005, 5(2): 215-238. doi: 10.3934/dcdsb.2005.5.215

Approximation of attractors of nonautonomous dynamical systems

Bernd Aulbach 1, , Martin Rasmussen 1, and  Stefan Siegmund 2,

1. 

Department of Mathematics, University of Augsburg, D-86135 Augsburg, Germany, Germany
2. 

Department of Mathematics, University of Frankfurt, D-60325 Frankfurt, Germany

Received  December 2003 Revised  July 2004 Published  February 2005

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.
Keywords: Continuation algorithm, Subdivision algorithm, Nonautonomous diference equation, Invariant manifold, Numerical approximation, Forward attractor, Nonautonomous bifurcation., Pullback attractor, Nonautonomous dynamical system.
Mathematics Subject Classification: 34C30, 34D45, 37B55, 37G35, 39A10, 65L2.
Citation: Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Approximation of attractors of nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems - B, 2005, 5 (2) : 215-238. doi: 10.3934/dcdsb.2005.5.215
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