Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors

Holger Kantz, Celso Grebogi, Awadhesh Prasad, Ying-Cheng Lai, Erik Sinde

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic attractors. Whereas in the presence of tangencies, interactive noise yields attractor deformations, attractors with only dimension variability are robust, despite the fact that shadowing is grossly violated.

Original languageEnglish (US)
Article number026209
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number2
DOIs
StatePublished - Feb 2002

Fingerprint

Noise Robustness
Chaotic Attractor
Attractor
Stable and Unstable Manifolds
Hausdorff Distance
Shadowing
Scaling Laws
Unstable
scaling laws
Class

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Unexpected robustness against noise of a class of nonhyperbolic chaotic attractors. / Kantz, Holger; Grebogi, Celso; Prasad, Awadhesh; Lai, Ying-Cheng; Sinde, Erik.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 65, No. 2, 026209, 02.2002.

Research output: Contribution to journalArticle

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