CLUSTERING IN GLOBALLY COUPLED PHASE OSCILLATORS
CLUSTERING IN GLOBALLY COUPLED PHASE OSCILLATORS
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DOI：
10.1103/physreva.45.3516
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发表时间：
1992-03-15
影响因子：
2.9
通讯作者：
SOMPOLINSKY, H
中科院分区：
文献类型：
--
作者：
GOLOMB, D;HANSEL, D;SOMPOLINSKY, H
采用解析和数值方法研究了多个全局耦合相位振荡器的模型。每个振子通过一个全局驱动力与所有其他振子耦合，驱动力的形式为SIGMA(j)g(phi(j))，其中g（phi(j)）是第j相的周期函数。分析了吸引子在参数空间各区域的时空特性。除了简单的空间均匀不动点和极限环外，该系统还表现出三种空间非均匀吸引子。第一种是集群状态，在这种状态下，系统分成几个宏观上的大集群，每个集群都是完全同步的。第二，存在全频率锁定但不锁相的稳态。相的分布在时间上是平稳的。第三，在一个极窄的参数范围内，存在一个非周期吸引子。研究发现，在弱随机噪声的作用下，聚类状态是稳定的。增加超过临界值的噪声水平会产生向平稳遍历状态的连续过渡。在动力学非线性只涉及一次谐波的特殊情况下，观察到边缘状态，其特征是连续的边缘稳定极限轨迹。这些状态在噪声的引入下是不稳定的。
A model of many globally coupled phase oscillators is studied by analytical and numerical methods. Each oscillator is coupled to all the other oscillators via a global driving force that takes the form SIGMA(j)g(phi(j)), where g(phi(j)) is a periodic function of the jth phase. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. In addition to simple spatially uniform fixed points and limit cycles, the system also exhibits spatially nonuniform attractors of three kinds. First, there are cluster states in which the system breaks into a few macroscopically big clusters, each of which is fully synchronized. Second, there is a stationary state with full frequency locking but no phase locking. The distribution of phases is stationary in time. Third, in an extremely narrow regime of parameters, a nonperiodic attractor exists. It is found that the cluster state is stable to the addition of weak stochastic noise. Increasing the level of noise beyond a critical value generates a continuous transition to a stationary ergodic state. In the special case where the nonlinearities in the dynamics involve only first harmonics, marginal states are observed, characterized by a continuum of marginally stable limit trajectories. These states are unstable under the introduction of noise.