Stability properties of nonhyperbolic chaotic attractors with respect to noise.

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.

• Publication year

  2004

• Venue

  Physical Review Letters

• Publication date

  2004-11-30

• Fields of study

  Medicine, Physics, Mathematics

• Identifiers
  DOI 10.1103/PhysRevLett.93.250603arXiv nlin/0411064PMID 15697888
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Escaping from nonhyperbolic chaotic attractors.

  2003cited by this paper
• Noise-level estimation of time series using coarse-grained entropy.

  2003cited by this paper
• Fluctuational transitions through a fractal basin boundary.

  2003cited by this paper
• Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors.

  2002cited by this paper
• Bayesian reconstruction of chaotic dynamical systems

  2000cited by this paper
• Dynamics of activated escape and its observation in a semiconductor laser

  2000cited by this paper
• Estimation of noise levels for models of chaotic dynamical systems

  2000cited by this paper
• Communication with chemical chaos in the presence of noise.

  1998cited by this paper
• Nonlinear noise reduction through Monte Carlo sampling.

  1998cited by this paper
• Noise reduction in chaotic time-series data: A survey of common methods.

  1993cited by this paper
• Large fluctuations and fluctuational transitions in systems driven by colored Gaussian noise: A high-frequency noise.

  1990cited by this paper
• Noise-induced escape from attractors in one-dimensional maps.

  1989cited by this paper
• Random Perturbations of Dynamical Systems

  1984cited by this paper

• Stochastic basin stability in complex networks

  2018cites this paper
• Effects of bounded random perturbations on discrete dynamical systems

  2013cites this paper
• Random fluctuation leads to forbidden escape of particles.

  2009cites this paper
• Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit.

  2009cites this paper
• Switching-path distribution in multidimensional systems.

  2008cites this paper
• Paths of fluctuation induced switching.

  2008cites this paper
• Effects of time delay on transient behavior of a time-delayed metastable system subjected to cross-correlated noises

  2008cites this paper
• Signatures of noise-enhanced stability in metastable states.

  2005cites this paper