Synchronization and Collective Motion of a Group of Weakly Coupled Identical Oscillators

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.