Solution of the boundary value problem for nonlinear flows and maps

Stefano Beri; Dmitrii G. Luchinsky; Alexandr Silchenko; Peter V.E. McClintock

doi:10.1117/12.489017

7 May 2003 Solution to the boundary values problem in chaotic flows and maps

Stefano Beri, Dmitrii G. Luchinsky, Alexandr Silchenko, Peter V.E. McClintock

Proceedings Volume 5114, Noise in Complex Systems and Stochastic Dynamics; (2003) https://doi.org/10.1117/12.489017
Event: SPIE's First International Symposium on Fluctuations and Noise, 2003, Santa Fe, New Mexico, United States

Abstract

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.

Citation Download Citation

Stefano Beri, Dmitrii G. Luchinsky, Alexandr Silchenko, and Peter V.E. McClintock "Solution to the boundary values problem in chaotic flows and maps", Proc. SPIE 5114, Noise in Complex Systems and Stochastic Dynamics, (7 May 2003); https://doi.org/10.1117/12.489017

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