The phenomena of synchronization for a large number of weakly coupled oscillators with dissipative couplings are studied. These couplings are taken into account in the system’s dynamic equations in the form of diffusion matrices, guaranteeing asymptotically stable oscillations of the ensemble as a whole. As illustrative examples, three types of interaction of oscillators are considered, namely, interaction with each other, interaction with the nearest neighbors, and circular interaction with the nearest neighbors.

中文翻译：

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一组弱耦合同振子的同步和集体运动

研究了具有耗散耦合的大量弱耦合振荡器的同步现象。在系统的动力学方程中，以扩散矩阵的形式考虑了这些耦合，从而确保了整体的渐近稳定振荡。作为说明性示例，考虑了振荡器的三种交互类型，即，彼此交互，与最近邻居的交互以及与最近邻居的循环交互。