On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm

Hüls T (2016)
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 26(7): 1650118.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We propose an algorithm for the approximation of stable and unstable fibers that applies to autonomous as well as to nonautonomous ODEs. The algorithm is based on computing the zero-contour of a specific operator; an idea that was introduced in [Huls, 2016] for discrete time systems. We present precise error estimates for the resulting contour algorithm and demonstrate its efficiency by computing stable and unstable fibers for a (non) autonomous pendulum equation in two space dimensions. Our second example is the famous three-dimensional Lorenz system for which several approximations of the two-dimensional Lorenz manifold are calculated. In both examples, we observe equally well performance for autonomously and nonautonomously chosen parameters.
Stichworte
Invariant fiber bundles; stable and unstable manifolds; numerical; approximation; contour algorithm; Lorenz system
Erscheinungsjahr
2016
Zeitschriftentitel
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Band
26
Ausgabe
7
Art.-Nr.
1650118
ISSN
0218-1274
eISSN
1793-6551
Page URI
https://pub.uni-bielefeld.de/record/2905976

Zitieren

Hüls T. On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2016;26(7): 1650118.
Hüls, T. (2016). On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 26(7), 1650118. https://doi.org/10.1142/S0218127416501182
Hüls, T. (2016). On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 26:1650118.
Hüls, T., 2016. On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 26(7): 1650118.
T. Hüls, “On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm”, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol. 26, 2016, : 1650118.
Hüls, T.: On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 26, : 1650118 (2016).
Hüls, Thorsten. “On the Approximation of Stable and Unstable Fiber Bundles of (Non) Autonomous ODEs - A Contour Algorithm”. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 26.7 (2016): 1650118.

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