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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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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25 Jan 2010 13:33
Last Modified:
12 Sep 2023 01:07