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 |
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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.
In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 67, No. 4, 01.01.2003.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 -