Approximation of attractors of nonautonomous dynamical systems
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
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.
Details
Original language | English |
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Pages (from-to) | 215-238 |
Number of pages | 24 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 5 |
Issue number | 2 |
Publication status | Published - May 2005 |
Peer-reviewed | Yes |
Externally published | Yes |
External IDs
ORCID | /0000-0003-0967-6747/work/149795386 |
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Keywords
ASJC Scopus subject areas
Keywords
- Continuation algorithm, Forward attractor, Fullback attractor, Invariant manifold, Nonautonomous bifurcation, Nonautonomous difference equation, Nonautonomous dynamical system, Numerical approximation, Subdivision algorithm