### Abstract

On-off intermittent chaotic behavior occurs in physical systems with symmetry. The phenomenon refers to the situation where one or more physical variables exhibit two distinct states in their time evolution. One is the ''off'' state where the physical variables remain constant, and the other is the ''on'' state where the variables temporarily burst out of the ''off'' state. We demonstrate that by using arbitrarily small feedback control to an accessible parameter or state of the system, the ''on'' state can be eliminated completely. This could be practically advantageous where the desirable operational state of the system is the ''off'' state. Relevant issues such as the influence of noise and the time required to achieve the control. are addressed. It is found that the average transient time preceding the control obeys a scaling law that is qualitatively different from the algebraic scaling law which occurs when one controls chaos by stabilizing unstable periodic orbits embedded in a chaotic attractor. A theoretical argument is provided for the observed scaling law.

Original language | English |
---|---|

Pages (from-to) | 1190-1199 |

Number of pages | 10 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 54 |

Issue number | 2 |

Publication status | Published - Aug 1996 |

### Keywords

- BELOUSOV-ZHABOTINSKY REACTION
- CONTROLLING CHAOS
- RIDDLED BASINS
- PROPORTIONAL FEEDBACK
- SYSTEMS
- ATTRACTORS
- SYNCHRONIZATION
- OSCILLATOR
- TRANSITION
- MOTION

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*54*(2), 1190-1199.

**Controlling on-off intermittent dynamics.** / Nagai, Y ; Hua, X D ; Lai, Y C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 54, no. 2, pp. 1190-1199.

}

TY - JOUR

T1 - Controlling on-off intermittent dynamics

AU - Nagai, Y

AU - Hua, X D

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1996/8

Y1 - 1996/8

N2 - On-off intermittent chaotic behavior occurs in physical systems with symmetry. The phenomenon refers to the situation where one or more physical variables exhibit two distinct states in their time evolution. One is the ''off'' state where the physical variables remain constant, and the other is the ''on'' state where the variables temporarily burst out of the ''off'' state. We demonstrate that by using arbitrarily small feedback control to an accessible parameter or state of the system, the ''on'' state can be eliminated completely. This could be practically advantageous where the desirable operational state of the system is the ''off'' state. Relevant issues such as the influence of noise and the time required to achieve the control. are addressed. It is found that the average transient time preceding the control obeys a scaling law that is qualitatively different from the algebraic scaling law which occurs when one controls chaos by stabilizing unstable periodic orbits embedded in a chaotic attractor. A theoretical argument is provided for the observed scaling law.

AB - On-off intermittent chaotic behavior occurs in physical systems with symmetry. The phenomenon refers to the situation where one or more physical variables exhibit two distinct states in their time evolution. One is the ''off'' state where the physical variables remain constant, and the other is the ''on'' state where the variables temporarily burst out of the ''off'' state. We demonstrate that by using arbitrarily small feedback control to an accessible parameter or state of the system, the ''on'' state can be eliminated completely. This could be practically advantageous where the desirable operational state of the system is the ''off'' state. Relevant issues such as the influence of noise and the time required to achieve the control. are addressed. It is found that the average transient time preceding the control obeys a scaling law that is qualitatively different from the algebraic scaling law which occurs when one controls chaos by stabilizing unstable periodic orbits embedded in a chaotic attractor. A theoretical argument is provided for the observed scaling law.

KW - BELOUSOV-ZHABOTINSKY REACTION

KW - CONTROLLING CHAOS

KW - RIDDLED BASINS

KW - PROPORTIONAL FEEDBACK

KW - SYSTEMS

KW - ATTRACTORS

KW - SYNCHRONIZATION

KW - OSCILLATOR

KW - TRANSITION

KW - MOTION

M3 - Article

VL - 54

SP - 1190

EP - 1199

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -