Efficient detection of periodic orbits in high dimensional systems

CROFTS, J.J. and DAVIDCHAK, R.L., 2005. Efficient detection of periodic orbits in high dimensional systems. In: ICNAAM 2005.

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Abstract

This paper is concerned with developing a method for detecting unstable periodic orbits (UPOs) by stabilising transformations. Here the strategy is to transform the system of interest in such away that the orbits become stable. However, the number of such transformations becomes overwhelming as we move to higher dimensions [5, 16, 17]. We have recently proposed a set of stabilising transformations which is constructed from a small set of already found UPOs [1]. The real value of the set is that its cardinality depends on the dimension of the unstable manifold at the UPO rather than the dimension of the system. Here we extend this approach to high dimensional systems of ODEs and apply it to the model example of a chaotic spatially extended system - the Kuramoto-Sivashinsky equation.

Item Type: Conference contribution
Creators: Crofts, J.J. and Davidchak, R.L.
Publisher: Wiley-VCH
Date: 2005
Rights: © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Divisions: Schools > School of Science and Technology
Depositing User: EPrints Services
Date Added: 09 Oct 2015 10:49
Last Modified: 09 Jun 2017 13:40
URI: http://irep.ntu.ac.uk/id/eprint/18557

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