Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2004-11-30
Nonlinear Sciences
Chaotic Dynamics
Phys.Rev. Lett., to be published
Scientific paper
10.1103/PhysRevLett.93.250603
We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal escape energy necessary to leave the basin of attraction, calculated with the Hamiltonian theory of large fluctuations. We establish the important and counterintuitive result that both concepts may be opposed to each other. Even when one attractor is globally more stable than another one, it can be locally less stable. Our results are exemplified with the Holmes map, for two different sets of parameter, and with a juxtaposition of the Holmes and the Ikeda maps. Finally, the experimental relevance of these findings is pointed out.
Grebogi Celso
Kraut Suso
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