Universal scaling of Lyapunov exponents in coupled chaotic oscillators

Zonghua Liu, Ying-Cheng Lai, Manuel A. Matías

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish (US)
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume67
Issue number4
DOIs
StatePublished - Jan 1 2003

Fingerprint

Chaotic Oscillator
Coupled Oscillators
Lyapunov Exponent
oscillators
exponents
Scaling
Scaling Laws
scaling
scaling laws
Lorenz attractor
Chaotic Attractor
set theory
Attractor
disturbances
Disturbance
trajectories
Trajectory
Subset
Zero

ASJC Scopus subject areas

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

Cite this

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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.

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