非线性耦合Rssler系统的相位同步化

Phase Synchronization Between Nonlinearly Coupled Rssler Systems

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.

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 lin- ear 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.