The numerical computation of connecting orbits in dynamical systems

Beyn W-J (1990)
IMA Journal of Numerical Analysis 10(3): 379-405.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Structural changes in dynamical systems are often related to the appearance or disappearance of orbits connecting two stationary points (either heteroclinic or homoclinic). Homoclinic orbits typically arise in one-parameter problems when on a branch of periodic solutions the periods tend to infinity (e.g. Guckenheimer & Holmes, 1983). We develop a direct numerical method for the computation of connecting orbits and their associated parameter values. We employ a general phase condition and truncate the boundary-value problem to a finite interval by using on both ends the technique of asymptotic boundary conditions; see, for example, de Hoog & Weiss (1980), Lentini & Keller (1980). The approximation error caused by this truncation is shown to decay exponentially. Based on this analysis and additional numerical investigations we set up an adaptive strategy for choosing the truncation interval.
Stichworte
phase condition; connecting orbits; stationary points; iterative method; dynamical systems
Erscheinungsjahr
1990
Zeitschriftentitel
IMA Journal of Numerical Analysis
Band
10
Ausgabe
3
Seite(n)
379-405
ISSN
0272-4979
eISSN
1464-3642
Page URI
https://pub.uni-bielefeld.de/record/1784254

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Beyn W-J. The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis. 1990;10(3):379-405.
Beyn, W. - J. (1990). The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis, 10(3), 379-405. doi:10.1093/imanum/10.3.379
Beyn, W. - J. (1990). The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis 10, 379-405.
Beyn, W.-J., 1990. The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis, 10(3), p 379-405.
W.-J. Beyn, “The numerical computation of connecting orbits in dynamical systems”, IMA Journal of Numerical Analysis, vol. 10, 1990, pp. 379-405.
Beyn, W.-J.: The numerical computation of connecting orbits in dynamical systems. IMA Journal of Numerical Analysis. 10, 379-405 (1990).
Beyn, Wolf-Jürgen. “The numerical computation of connecting orbits in dynamical systems”. IMA Journal of Numerical Analysis 10.3 (1990): 379-405.
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