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Cooperative phenomena observed in a globally coupled phase-locked loop system

机译:在全局耦合锁相环系统中观察到的合作现象

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The authors describe cooperative phenomena observed in a globally coupled 8-phase-locked loop (PLL) system in both experiments and simulations by using SPICE. In the present system, each PLL is connected through the coupler that averages the all PLLs' output signals. When the frequency modulated external force is applied, three phases are observed such as (1) the coherent phase in which all subsystems are synchronized, (2) the turbulent phase in which all subsystems oscillate independently, and (3) the partially synchronized phase in which creation of clusters and chaotic itineracy due to the reconstruction of clusters occur. In the partially synchronized phase, the time series of voltage difference between arbitrary two subsystems shows an intermittency. From the statistical analysis for this intermittency it is found that the distribution functions of burst amplitude and laminar duration time show the -1 power law and -1.5 power law, respectively. These properties agree with those of the on-off intermittency. We also investigate the variation of number of cluster in the partially synchronized phase. The distribution function of the duration time of one-cluster state, namely the residence time in the state in which all subsystems are synchronized with each other, is also expressed as the -1.5 power law.
机译:作者描述了使用SPICE在实验和仿真中在全局耦合8锁相环(PLL)系统中观察到的协作现象。在本系统中,每个PLL通过耦合器连接,该耦合器对所有PLL的输出信号求平均。当施加调频外力时,观察到三个阶段,例如(1)所有子系统都同步的相干相位;(2)所有子系统独立地振荡的湍流相位;(3)各个相位同步的相位。发生簇的创建以及由于簇的重建而导致的混乱迭代。在部分同步阶段,任意两个子系统之间的电压差的时间序列显示出间歇性。通过对这种间歇性的统计分析,发现突发幅度和层流持续时间的分布函数分别显示-1幂定律和-1.5幂定律。这些属性与开关间歇性一致。我们还研究了部分同步阶段中簇数的变化。一簇状态的持续时间的分布函数,即在所有子系统彼此同步的状态下的停留时间,也表示为-1.5幂定律。

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