Experiments on oscillator ensembles with global nonlinear coupling
Experiments on oscillator ensembles with global nonlinear coupling
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DOI：
10.1103/physreve.85.015204
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发表时间：
2012-01-31
影响因子：
2.4
通讯作者：
Rosenblum, Michael
中科院分区：
文献类型：
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作者：
Temirbayev, Amirkhan A.;Zhanabaev, Zeinulla Zh.;Rosenblum, Michael
我们实验分析了20个电子维恩桥极限环振荡器的集体动力学与非线性相移单元的全球反馈回路。随着耦合强度的增加，我们首先观察到的同步集群的形成，然后破坏，使序参量的耦合强度的依赖关系是不单调的。在簇被破坏之后，集合仍然保持相干，即，它表现出振荡集体模式（平均场）。我们表明，该系统现在是在一个自组织的准周期状态，预测在Rosenblum和Pikovsky [物理。98，064101（2007）]。在这种状态下，所有振荡器的频率都小于平均场的频率，因此振荡器不会锁定在它们所产生的平均场上，并且它们的动力学是准周期的。在没有非线性相移单元的情况下，系统表现出标准的Kuramoto式过渡到完全同步状态。我们证明了实验和以前开发的理论之间的良好对应关系。我们还提出了一个简单的措施，其特点的宏观非相干相干过渡的有限大小的合奏。
We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.