Solution of the boundary value problem for nonlinear flows and maps

Beri, Stefano and Luchinsky, Dmitrii G. and Silchenko, Alexander and McClintock, Peter V. E. (2003) Solution of the boundary value problem for nonlinear flows and maps. Proceedings of SPIE, 5114. pp. 372-382. ISSN 0277-786X

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Fluctuational escape via an unstable limit cycle is investigated in stochastic flows and maps. A new topological method is suggested for analysis of the corresponding boundary value problems when the action functional has multiple local minima along the escape trajectories and the search for the global minimum is otherwise impossible. The method is applied to the analysis of the escape problem in the inverted Van der Pol oscillator and in the Henon map. An application of this technique to solution of the escape problem in chaotic maps with fractal boundaries, and in maps with chaotic saddles embedded within the basin of attraction, is discussed.

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Proceedings of SPIE
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Copyright 2003 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
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04 Jul 2008 10:30
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15 Sep 2023 04:12