### Abstract

We have uncovered a phenomenon in coupled chaotic oscillators where a subset of Lyapunov exponents, which are originally zero in the absence of coupling, can become positive as the coupling is increased. This occurs for chaotic attractors having multiple scrolls, such as the Lorenz attractor. We argue that the phenomenon is due to the disturbance to the relative frequencies with which a trajectory visits different scrolls of the attractor. An algebraic scaling law is obtained which relates the Lyapunov exponents with the coupling strength. The scaling law appears to be universal.

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

Number of pages | 1 |

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

Volume | 67 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2003 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Universal scaling of Lyapunov exponents in coupled chaotic oscillators.** / Liu, Zonghua; Lai, Ying-Cheng; Matías, Manuel A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Universal scaling of Lyapunov exponents in coupled chaotic oscillators

AU - Liu, Zonghua

AU - Lai, Ying-Cheng

AU - Matías, Manuel A.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - We have uncovered a phenomenon in coupled chaotic oscillators where a subset of Lyapunov exponents, which are originally zero in the absence of coupling, can become positive as the coupling is increased. This occurs for chaotic attractors having multiple scrolls, such as the Lorenz attractor. We argue that the phenomenon is due to the disturbance to the relative frequencies with which a trajectory visits different scrolls of the attractor. An algebraic scaling law is obtained which relates the Lyapunov exponents with the coupling strength. The scaling law appears to be universal.

AB - We have uncovered a phenomenon in coupled chaotic oscillators where a subset of Lyapunov exponents, which are originally zero in the absence of coupling, can become positive as the coupling is increased. This occurs for chaotic attractors having multiple scrolls, such as the Lorenz attractor. We argue that the phenomenon is due to the disturbance to the relative frequencies with which a trajectory visits different scrolls of the attractor. An algebraic scaling law is obtained which relates the Lyapunov exponents with the coupling strength. The scaling law appears to be universal.

UR - http://www.scopus.com/inward/record.url?scp=85037228321&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037228321&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.67.045203

DO - 10.1103/PhysRevE.67.045203

M3 - Article

AN - SCOPUS:85037228321

VL - 67

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

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

SN - 1539-3755

IS - 4

ER -