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Energy-optimal steering of transitions through a fractal basin boundary.

Silchenko, A. N. and Beri, S. and Luchinsky, D. G. and McClintock, Peter V. E. (2004) Energy-optimal steering of transitions through a fractal basin boundary. In: International Proceedings of Conference on Physics and Control, PHYSCON-2003. IEEE, New York, pp. 501-506. ISBN 0-7803-7939-X

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    Abstract

    We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states.

    Item Type: Contribution in Book/Report/Proceedings
    Additional Information: "©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." "This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."
    Subjects: Q Science > QC Physics
    Departments: Faculty of Science and Technology > Physics
    ID Code: 31486
    Deposited By: Professor P. V. E. McClintock
    Deposited On: 25 Jan 2010 13:33
    Refereed?: No
    Published?: Published
    Last Modified: 26 Jul 2012 21:43
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/31486

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