### Abstract

Snapshot attractors, i.e., attractors formed by a cloud of trajectories at the same instants of time, are usually employed to reveal the fractal structure of randomly or chaotically driven dynamical systems. A necessary condition for the underlying fractal structure to be observed is that the ensemble of particles utilized in the construction of the snapshot attractors are subject to identical perturbation at any instant of time. We examine the influence of small phase-space inhomogeneity in the chaotic perturbation on the observability of the snapshot fractal attractors. We find that, typically, fractal structure can be seen in only a transient period of time. The scaling of the transient time with the amount of inhomogeneity is investigated. Implication to experimental observation of fractal structure in physical systems is pointed out.

Original language | English (US) |
---|---|

Pages (from-to) | 1558-1562 |

Number of pages | 5 |

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

Volume | 60 |

Issue number | 2 B |

State | Published - 1999 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

**Transient fractal behavior in snapshot attractors of driven chaotic systems.** / Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 60, no. 2 B, pp. 1558-1562.

}

TY - JOUR

T1 - Transient fractal behavior in snapshot attractors of driven chaotic systems

AU - Lai, Ying-Cheng

PY - 1999

Y1 - 1999

N2 - Snapshot attractors, i.e., attractors formed by a cloud of trajectories at the same instants of time, are usually employed to reveal the fractal structure of randomly or chaotically driven dynamical systems. A necessary condition for the underlying fractal structure to be observed is that the ensemble of particles utilized in the construction of the snapshot attractors are subject to identical perturbation at any instant of time. We examine the influence of small phase-space inhomogeneity in the chaotic perturbation on the observability of the snapshot fractal attractors. We find that, typically, fractal structure can be seen in only a transient period of time. The scaling of the transient time with the amount of inhomogeneity is investigated. Implication to experimental observation of fractal structure in physical systems is pointed out.

AB - Snapshot attractors, i.e., attractors formed by a cloud of trajectories at the same instants of time, are usually employed to reveal the fractal structure of randomly or chaotically driven dynamical systems. A necessary condition for the underlying fractal structure to be observed is that the ensemble of particles utilized in the construction of the snapshot attractors are subject to identical perturbation at any instant of time. We examine the influence of small phase-space inhomogeneity in the chaotic perturbation on the observability of the snapshot fractal attractors. We find that, typically, fractal structure can be seen in only a transient period of time. The scaling of the transient time with the amount of inhomogeneity is investigated. Implication to experimental observation of fractal structure in physical systems is pointed out.

UR - http://www.scopus.com/inward/record.url?scp=0005154445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005154445&partnerID=8YFLogxK

M3 - Article

VL - 60

SP - 1558

EP - 1562

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2 B

ER -