非线性耦合Rössler系统的相位同步化

刘勇; 毕勤胜; 陈予恕

非线性耦合Rössler系统的相位同步化

1.
江苏大学理学院,江苏镇江 212013;2.盐城师范学院数学科学学院,江苏盐城 224002;3.哈尔滨工业大学,哈尔滨 150001

基金项目: 国家自然科学基金资助项目(2047604110602020)

详细信息

作者简介:
刘勇(1973- ),男,江苏盐城人,博士;毕勤胜,教授(联系人.Tel:+86-511-88791110;E-mail:qbi@ujs.edu.cn).

中图分类号: O193
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- 被引次数: 0
出版历程
- 收稿日期: 2007-10-26
- 修回日期: 2008-04-14
- 刊出日期: 2008-06-15

Phase Synchronization Between Nonlinearly Coupled R^L ssler Systems

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

摘要

摘要: 讨论了具有1∶1和1∶2内共振非线性耦合系统的混沌相位同步．通过引入混沌运动的相位定义说明对于不同的内共振系统，在相对小的参数下两个子系统的平均频率差接近于0，即在弱相互作用下两个振子相位同步．随着耦合力的增加，平均频率差有波动，与1∶2内共振情形相比，在主共振条件下两个子系统平均频率差的波动较小，即使在弱作用下也是如此．线性耦合力的增加增强了相位同步效应，而非线性耦合力的增加使得两个子系统由相位同步向不同步转化，且相位动力学与Liapunov的变化有关，这也可以通过扩散云图来证实．
- 相位同步 /
- Rssler振子 /
- 非线性耦合 /
- Liapunov指数
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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