Rights statement: Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in AIP Conference Proceedings, 665, 2003 and may be found at http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.1584918
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Research output: Contribution to Journal/Magazine › Journal article
Research output: Contribution to Journal/Magazine › Journal article
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TY - JOUR
T1 - Fluctuational escape from chaotic attractors
AU - Khovanov, Igor A.
AU - Luchinsky, D. G.
AU - Mannella, R.
AU - McClintock, Peter V. E.
AU - Silchenko, Alexander N.
N1 - Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in AIP Conference Proceedings, 665, 2003 and may be found at http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.1584918
PY - 2003
Y1 - 2003
N2 - Fluctuational transitions between two coexisting attractors are investigated. Two different systems are considered: the periodically driven nonlinear oscillator and the two‐dimensional map introduced by Holmes. These two systems have smooth and fractal boundaries, respectively, separating their coexisting attractors. It is shown that, starting from a cycle embedded in the chaotic attractor, the periodically‐driven oscillator escapes to a saddle cycle at the boundary of the basin of attraction, and does so through sequential transitions between saddles cycles embedded in the attractor. In the case of discrete dynamics with locally disconnected fractal boundaries, it is shown that escape from an attractor always seems to occur through an accessible boundary orbit and further through the specific homoclinic points forming a fractal structure of the boundary. It is shown that analysis of fluctuational transitions between attractors can be used to solve a problem of the energy‐optimal migration of a chaotic system. The deterministic optimal control functions are identified with the corresponding optimal fluctuational forces in the limit of small noise intensity. We discuss possible applications and related unsolved problems of stochastic dynamics.
AB - Fluctuational transitions between two coexisting attractors are investigated. Two different systems are considered: the periodically driven nonlinear oscillator and the two‐dimensional map introduced by Holmes. These two systems have smooth and fractal boundaries, respectively, separating their coexisting attractors. It is shown that, starting from a cycle embedded in the chaotic attractor, the periodically‐driven oscillator escapes to a saddle cycle at the boundary of the basin of attraction, and does so through sequential transitions between saddles cycles embedded in the attractor. In the case of discrete dynamics with locally disconnected fractal boundaries, it is shown that escape from an attractor always seems to occur through an accessible boundary orbit and further through the specific homoclinic points forming a fractal structure of the boundary. It is shown that analysis of fluctuational transitions between attractors can be used to solve a problem of the energy‐optimal migration of a chaotic system. The deterministic optimal control functions are identified with the corresponding optimal fluctuational forces in the limit of small noise intensity. We discuss possible applications and related unsolved problems of stochastic dynamics.
U2 - 10.1063/1.1584918
DO - 10.1063/1.1584918
M3 - Journal article
VL - 665
SP - 435
EP - 442
JO - AIP Conference Proceedings
JF - AIP Conference Proceedings
SN - 0094-243X
ER -