PMID: 12786425Jun 6, 2003Paper

Universal scaling of Lyapunov exponents in coupled chaotic oscillators

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Zonghua LiuManuel A Matías

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.

References

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Citations

Jul 11, 2006·Chaos·Shuguang GuanC-H Lai
Mar 9, 2004·Chaos·Ying-Cheng Lai, Zonghua Liu
Aug 5, 2016·Scientific Reports·Wenlin LiHeshan Song
Feb 3, 2004·Physical Review Letters·Mukeshwar DhamalaMingzhou Ding
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Oleksandr V PopovychPeter A Tass
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shuguang GuanG W Wei
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jie Zhou, Zonghua Liu
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Douglas ZhouDavid Cai
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rosangela FollmannEpaminondas Rosa
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Liang ZhaoChih-Wen Shih
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yan WangZhigang Zheng
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G X QiY J Zhang
Apr 4, 2021·Chaos·Ken-Ichi Okubo, Ken Umeno

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