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

Research output: Contribution in Book/Report/ProceedingsChapter

Published

Publication date14/10/2004
Host publicationInternational Proceedings of Conference on Physics and Control, PHYSCON-2003
Place of publicationNew York
PublisherIEEE
Pages501-506
Number of pages6
Volume2
ISBN (Print)0-7803-7939-X
Original languageEnglish

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.

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