### Abstract

We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether,the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise-when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

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

Pages (from-to) | 57-65 |

Number of pages | 9 |

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

Volume | 53 |

Issue number | 1 |

Publication status | Published - Jan 1996 |

### Keywords

- DYNAMICAL-SYSTEMS
- TURBULENCE
- CRISES
- FLUID

### Cite this

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

*53*(1), 57-65.

**Transition from strange nonchaotic to strange chaotic attractors.** / Lai, Y C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 1, pp. 57-65.

}

TY - JOUR

T1 - Transition from strange nonchaotic to strange chaotic attractors

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1996/1

Y1 - 1996/1

N2 - We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether,the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise-when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

AB - We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether,the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise-when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

KW - DYNAMICAL-SYSTEMS

KW - TURBULENCE

KW - CRISES

KW - FLUID

M3 - Article

VL - 53

SP - 57

EP - 65

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 - 1

ER -