Synchronized clusters and multistability in arrays of oscillators with different natural frequencies

The collective effects in arrays of diffusively coupled Van der Pol oscillators with different natural frequencies are investigated by asymptotic and numerical methods. The conditions for the onset and existence of the regimes of global (all-to-all) and cluster (inside several subsets of elements) frequency synchronization are determined. It is found that there exist monostable and multistable regimes of cluster synchronization and the respective “soft” and “hard” transitions between the structures consisting of a different number of clusters. It is revealed that the synchronization is observed in a broader range of parameters in a randomly formed array than for regularly arranged oscillators with the natural frequencies varying monotonically along the array.