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

Research output: Contribution to journalJournal article

Published

Journal publication date2003
JournalApplied Nonlinear Dynamics
Journal number3
Volume11
Number of pages7
Pages38-44
Original languageEnglish

Abstract

We study fluctuational transitions in a discrete dynamical system that has two coexisting attractors in phase space, separated by a fractal basin boundary which may be either locally-disconnected or locally-connected. It is shown that, in each case, transitions occur via an accessible point on the boundary. The complicated structure of paths inside the locally-disconnected fractal boundary is determined by a hierarchy of homoclinic original saddles. The most probable escape path to the fractal boundary is found for each type of boundary using both statistical analyses of fluctuational trajectories and the Hamiltonian theory of fluctuations.