Universal scaling of Lyapunov exponents in coupled chaotic oscillators

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

Volumn 67, Issue 4 2, 2003, Pages 452031-452034

  Liu, Zonghua ^a   Lai, Ying Cheng ^a,b   Matías, Manuel A ^c  

^a ARIZONA STATE UNIVERSITY   (United States)

^b Campus Universitat Illes Balears ^*  (United States)

^c UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; LYAPUNOV METHODS; OSCILLATORS (ELECTRONIC); STATISTICAL METHODS;

CHAOTIC OSCILLATORS;

CHAOS THEORY;

EID: 0037866577     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

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9. Some pioneering studies on the scaling behavior of the largest Lyapunov exponent in coupled map lattices can be found, for example, in R. Livi, A. Politi, and S. Ruffo, J. Phys. A 25, 4813 (1992); W. Yang, E.-J. Ding, and M. Ding, Phys. Rev. Lett. 76, 1808 (1996); A. Torcini, R. Livi, A. Politi, and S. Ruffo, ibid. 78, 1391 (1997).
10. Some pioneering studies on the scaling behavior of the largest Lyapunov exponent in coupled map lattices can be found, for example, in R. Livi, A. Politi, and S. Ruffo, J. Phys. A 25, 4813 (1992); W. Yang, E.-J. Ding, and M. Ding, Phys. Rev. Lett. 76, 1808 (1996); A. Torcini, R. Livi, A. Politi, and S. Ruffo, ibid. 78, 1391 (1997).
11. Some pioneering studies on the scaling behavior of the largest Lyapunov exponent in coupled map lattices can be found, for example, in R. Livi, A. Politi, and S. Ruffo, J. Phys. A 25, 4813 (1992); W. Yang, E.-J. Ding, and M. Ding, Phys. Rev. Lett. 76, 1808 (1996); A. Torcini, R. Livi, A. Politi, and S. Ruffo, ibid. 78, 1391 (1997).
12. Typical trajectories restricted to "L" or "R" are transiently chaotic. It has been known that nonattracting chaotic saddles, which are responsible for transient chaos, are the "skeleton" of a chaotic attractor [K.G. Szabo and T. Tél, Phys. Rev. E 50, 1070 (1994)]. The pseudo-Lyapunov exponents can thus be defined with respect to the conditional measure for transient chaos [T. Tél, in Directions in Chaos, edited by B.-L. Hao (World Scientific, Singapore, 1990), Vol. 3).
13. Typical trajectories restricted to "L" or "R" are transiently chaotic. It has been known that nonattracting chaotic saddles, which are responsible for transient chaos, are the "skeleton" of a chaotic attractor [K.G. Szabo and T. Tél, Phys. Rev. E 50, 1070 (1994)]. The pseudo-Lyapunov exponents can thus be defined with respect to the conditional measure for transient chaos [T. Tél, in Directions in Chaos, edited by B.-L. Hao (World Scientific, Singapore, 1990), Vol. 3).
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15. R. Diestel, Graph Theory (Springer, New York, 2000).
16. In a future paper, we will give a detailed account of our physical scaling theory and provide extensive numerical check for the scaling law covering a wide array of coupling configurations. We also believe that results in this paper can be tested in experiments using chaotic electronic circuits.