耦合分段线性系统完全同步的一种途径

Transition to complete synchronization via coexistence of period clusters in coupled piecewise linear maps

目的 研究耦合分段线性映射的集体动力学行为随耦合强度的转迁过程及途径,进一步解释耦合系统同步过程的相变动力学。方法 通过计算耦合系统最大Lyapunov指数、平均序参量和同步概率刻画耦合分段线性映射的集体动力学行为与特征。结果与结论 耦合系统集体动力学呈现出混沌部分同步、周期同步集团、周期同步集团共存等丰富的动力学行为。研究表明,周期同步集团由2个共存的周期吸引子组成,且周期轨道是原系统的不稳定周期轨道,在局部非线性动力学项和空间耦合项相互作用下不稳定轨道达到动态平衡。结果揭示了在耦合分段线性映射系统中存在由周期同步集团共存到完全同步的一种新的转迁途径。

Purposes—To study the transition process and path of the collective dynamics of the coupled piecewise linear maps with respect to the coupling strength,and the further study of the dynamic phase transition of the synchronization process with the results.Methods—The largest Lyapunov exponents,along with the average order parameters and synchronization probability are calculated to characterize the collective dynamics and features of coupled piecewise linear maps.Results and Conclusions—It is shown that the increase of the coupling strength leads to period clusters,then induces a transition process from coexistence of period clusters to synchronization states,and the coupled system achieves complete synchronization.A detailed research shows the period clusters consist of two coexist period attractors,of which period orbit are two unstable periodic orbits of isolate map,and those unstable periodic orbits are re-stabilized as a result of the mutual interactions of the local nonlinearity.The spatial coupling sequential transitions to synchronization reveal a new transition route from coexistence of period clusters to complete synchronization in coupled piecewise linear map systems,and the results show a universal behavior in coupled piecewise linear systems.