### 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 language | English |
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Pages (from-to) | 105-109 |

Number of pages | 5 |

Journal | Physics Letters A |

Volume | 153 |

Issue number | 2-3 |

Publication status | Published - 25 Feb 1991 |

### Keywords

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

### Cite this

*Physics Letters A*,

*153*(2-3), 105-109.

**EXPERIMENTAL CONFIRMATION OF THE THEORY FOR CRITICAL EXPONENTS OF CRISES.** / SOMMERER, J C ; DITTO, W L ; GREBOGI, C ; OTT, E ; SPANO, M L .

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 153, no. 2-3, pp. 105-109.

}

TY - JOUR

T1 - EXPERIMENTAL CONFIRMATION OF THE THEORY FOR CRITICAL EXPONENTS OF CRISES

AU - SOMMERER, J C

AU - DITTO, W L

AU - GREBOGI, C

AU - OTT, E

AU - SPANO, M L

PY - 1991/2/25

Y1 - 1991/2/25

N2 - 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.

AB - 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.

KW - INDUCED INTERMITTENCY

KW - CHAOTIC ATTRACTORS

KW - TRANSIENT CHAOS

KW - NOISE

KW - OSCILLATOR

M3 - Article

VL - 153

SP - 105

EP - 109

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 2-3

ER -