Phase Synchronization Between Nonlinearly Coupled R<sup>L</sup> ssler Systems

LIU Yong; BI Qin-sheng; CHEN Yu-shu

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(6): 631-638

LIU Yong, BI Qin-sheng, CHEN Yu-shu. Phase Synchronization Between Nonlinearly Coupled RL ssler Systems[J]. Applied Mathematics and Mechanics, 2008, 29(6): 631-638.

Citation:

LIU Yong, BI Qin-sheng, CHEN Yu-shu. Phase Synchronization Between Nonlinearly Coupled R^L ssler Systems[J]. Applied Mathematics and Mechanics, 2008, 29(6): 631-638.

LIU Yong, BI Qin-sheng, CHEN Yu-shu. Phase Synchronization Between Nonlinearly Coupled RL ssler Systems[J]. Applied Mathematics and Mechanics, 2008, 29(6): 631-638.

Citation:

LIU Yong, BI Qin-sheng, CHEN Yu-shu. Phase Synchronization Between Nonlinearly Coupled R^L ssler Systems[J]. Applied Mathematics and Mechanics, 2008, 29(6): 631-638.

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Phase Synchronization Between Nonlinearly Coupled R^L ssler Systems

1.
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, P. R. China;

Received Date: 2007-10-26
Rev Recd Date: 2008-04-14
Publish Date: 2008-06-15

Abstract

Abstract

Phase synchronization between nonlinearly coupled systems with 1:1 and 1:2 resonances is investigated. By introducing the conception of phase for a chaotic motion, it demonstrates that for the different internal resonances, with relatively small parameter epsilon, both differences between the mean frequencies of the two sub-oscillators approach zero, implying phase synchronization can be achieved for weak interaction between the two oscillators. With the increase of the coupling strength, fluctuations of the frequency difference can be observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared with the case with frequency ratio 1:2, even with weak coupling strength. Unlike the enhance effect on the synchronization for linear coupling, the increase of nonlinear coupling strength results in the transition from phase synchronization to non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Liapunov exponents, which can also be explained by the diffuse clouds.
- phase synchronization,
- R? ssler oscillator,
- nonlinearly coupled,
- Liapunov exponent

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References(27)

References

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