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Numerical continuation of symmetric periodic orbits

Wulff, C and Schebesch, A (2006) Numerical continuation of symmetric periodic orbits SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 5 (3). 435 - 475. ISSN 1536-0040

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Abstract

The bifurcation theory and numerics of periodic orbits of general dynamical systems is well developed, and in recent years there has been rapid progress in the development of a bifurcation theory for symmetric dynamical systems. However, there are hardly any results on the numerical computation of those bifurcations yet. In this paper we show how spatio-temporal symmetries of periodic orbits can be exploited numerically. We describe methods for the computation of symmetry breaking bifurcations of periodic orbits for free group actions and show how bifurcations increasing the spatio-temporal symmetry of periodic orbits ( including period halving bifurcations and equivariant Hopf bifurcations) can be detected and computed numerically. Our pathfollowing algorithm is based on a multiple shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincare section and a tangential continuation method with implicit reparametrization.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Physics, Mathematical, Mathematics, Physics, numerical continuation, symmetry breaking bifurcations, symmetric periodic orbits, BIFURCATION, POINTS
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:42
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1550

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