### Abstract

Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive. Small random noise is incapable of causing characteristic changes in the Lyapunov spectrum, but it can make the attractor geometrically strange by dynamically connecting the original periodic attractor with the chaotic saddle. Here we present a detailed study of noise-induced SNAs and the characterization of their properties. Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers. An interesting finding is that the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution, the generality of which we are able to establish by a theoretical analysis using random matrices. We suggest a possible experimental test. We expect noise-induced SNAs to be general.

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

Article number | 016203 |

Pages (from-to) | - |

Number of pages | 11 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 74 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2006 |

### Keywords

- PERIODICALLY DRIVEN SYSTEMS
- FORCED SYSTEMS
- RANDOM MAPS
- TRANSITION
- CHAOS
- DYNAMICS
- BIRTH
- SYNCHRONIZATION
- SPECTRA
- CRISIS

### Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*74*(1), -. [016203]. https://doi.org/10.1103/PhysRevE.74.016203

**Characterization of noise-induced strange nonchaotic attractors.** / Wang, Xingang; Lai, Ying-Cheng; Lai, Choy Heng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 74, no. 1, 016203, pp. -. https://doi.org/10.1103/PhysRevE.74.016203

}

TY - JOUR

T1 - Characterization of noise-induced strange nonchaotic attractors

AU - Wang, Xingang

AU - Lai, Ying-Cheng

AU - Lai, Choy Heng

PY - 2006/7

Y1 - 2006/7

N2 - Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive. Small random noise is incapable of causing characteristic changes in the Lyapunov spectrum, but it can make the attractor geometrically strange by dynamically connecting the original periodic attractor with the chaotic saddle. Here we present a detailed study of noise-induced SNAs and the characterization of their properties. Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers. An interesting finding is that the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution, the generality of which we are able to establish by a theoretical analysis using random matrices. We suggest a possible experimental test. We expect noise-induced SNAs to be general.

AB - Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive. Small random noise is incapable of causing characteristic changes in the Lyapunov spectrum, but it can make the attractor geometrically strange by dynamically connecting the original periodic attractor with the chaotic saddle. Here we present a detailed study of noise-induced SNAs and the characterization of their properties. Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers. An interesting finding is that the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution, the generality of which we are able to establish by a theoretical analysis using random matrices. We suggest a possible experimental test. We expect noise-induced SNAs to be general.

KW - PERIODICALLY DRIVEN SYSTEMS

KW - FORCED SYSTEMS

KW - RANDOM MAPS

KW - TRANSITION

KW - CHAOS

KW - DYNAMICS

KW - BIRTH

KW - SYNCHRONIZATION

KW - SPECTRA

KW - CRISIS

U2 - 10.1103/PhysRevE.74.016203

DO - 10.1103/PhysRevE.74.016203

M3 - Article

VL - 74

SP - -

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

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

SN - 1539-3755

IS - 1

M1 - 016203

ER -