ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Silchenko A. N., Beri S., Luchinsky D. G., McClintock P. Fluctuational transitions across locally-disconnected and locally-connected fractal basin boundaries. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 3, pp. 38-45. DOI: 10.18500/0869-6632-2003-11-3-38-45

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Language: 
English
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
519.6: 537.86:519.2
DOI: 
10.18500/0869-6632-2003-11-3-38-45

Fluctuational transitions across locally-disconnected and locally-connected fractal basin boundaries

Autors: 
Silchenko Alexander Nikolaevich, Lancaster University
Beri Stefano, Lancaster University
Luchinsky Dmitrii G., Lancaster University
McClintock Peter Vaughan Elsmere, Lancaster University
Abstract: 

We study fluctuational transitions in а discrete dynamical system that has two coexisting attractors in phase space, separated by а fractal basin boundary which may be cither locally-disconnected оr locaily-connected. It is shown that, in each case, transitions оссur via аn accessible point оn the boundary. The complicated structure of paths inside the locally-disconnecied fractal boundary is determined by а hierarchy of homoclinic original saddles. The most probable escape path from а regular attractor to the fractal boundary is found for the each type of boundary using both statistical analyses of fluctuational trajectories and the Hamiltonian theory оf fluctuations.

Key words: 
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Acknowledgments: 
The research has been supported by the Engineering аnd Physical Sciences Research Council (UK) and INTAS.
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Received: 
01.08.2003
Accepted: 
15.09.2003
Available online: 
23.11.2023
Published: 
31.12.2003
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