环形网络中受挫Kuramoto振子的多稳定性与杂耍态
Multistability and Juggling States in Frustrated Kuramoto Oscillators on Ring Networks
- Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas（坎皮纳斯州立大学格列布·瓦塔金物理研究所）
- Departamento de Ciências da Computação, Universidade Estadual de Montes Claros（蒙蒂斯克拉鲁斯州立大学计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究分析环形网络中受挫Kuramoto振子的多稳定性与杂耍态，揭示交替序、顺序有序聚集体等同步解的特性及界面移动、聚集体湮灭等动力学行为。
AI中文摘要：
我们研究环形网络中矩阵耦合振子的特性，表明该系统支持多类同步聚化解。其中一类以连续振子属于不同聚集体为特征，称为交替序，包含两类解：第一类由1或2个静态聚集体组成，尽管存在非零自然振荡频率，其锁定的相位仍依赖于耦合参数；第二类由刚性旋转的聚集体组成，聚集体数量取决于邻接连通性。我们还研究了顺序有序聚集体，表明界面振子施加的约束对平衡构型有额外限制。尽管部分解是稳定的，但其吸引域依赖于模型参数：当系统以随机相位初始化时，振子倾向于自组织成动态聚集体，其界面沿环移动；每个聚集体内的振子保持接近某一稳定相位构型，而粒子在界面处交换。当反向移动的界面碰撞时，对应聚集体湮灭，直至达到界面沿同一方向移动的状态。
英文摘要：
We study the properties of matrix coupled oscillators in ring networks and show that the system supports several families of synchronized clustered solutions. One of these families is characterized by consecutive oscillators belonging to distinct clusters, called alternate ordering, with two classes of solutions. The first consists of one or two static clusters, that lock on phases that depend on the coupling parameters, despite the non-zero natural oscillation frequency. The second one is comprised of clusters that rotate rigidly. The number of clusters depends on the neighbor connectivity. We also investigated sequential ordered clusters and showed that the constraints imposed by the interface oscillators imposes additional restrictions to equilibrium configurations. Although some of these solutions are stable, their basins of attraction depend on model parameters: when the system is initialized with random phases, the oscillators tend to organize themselves into dynamical clusters whose interfaces move along the ring. The oscillators within each cluster remain close to one of the stable phase configurations, while particles are exchanged at the interfaces. When interfaces moving in opposite directions collide, the corresponding clusters annihilate, until a state with interfaces moving in a common direction is reached.
