EXPERIMENTAL CONFIRMATION OF THE THEORY FOR CRITICAL EXPONENTS OF CRISES

J C SOMMERER, W L DITTO, C GREBOGI, E OTT, M L SPANO

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Abstract

We investigate the scaling of the average time tau between intermittent bursts for a chaotic system that undergoes a homoclinic tangency crisis, which causes a sudden expansion in the attractor. The system studied is a periodically driven (frequency f), nonlinear, magnetoelastic ribbon. The observed behavior of tau is well fit by a power-law scaling tau approximately \f-f(c)\-gamma, where f = f(c) at the crisis. We identify the unstable periodic orbit mediating the crisis, and determine its linearized eigenvalues from experimental data. The critical exponent gamma found from the scaling of tau is shown to agree with that theoretically predicted for a two-dimensional map on the basis of the eigenvalues of the mediating periodic orbit.

Original languageEnglish
Pages (from-to)105-109
Number of pages5
JournalPhysics Letters A
Volume153
Issue number2-3
Publication statusPublished - 25 Feb 1991

Keywords

  • INDUCED INTERMITTENCY
  • CHAOTIC ATTRACTORS
  • TRANSIENT CHAOS
  • NOISE
  • OSCILLATOR

Cite this

SOMMERER, J. C., DITTO, W. L., GREBOGI, C., OTT, E., & SPANO, M. L. (1991). EXPERIMENTAL CONFIRMATION OF THE THEORY FOR CRITICAL EXPONENTS OF CRISES. Physics Letters A, 153(2-3), 105-109.