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

The collective effects in arrays of diffusively coupled Van der Pol oscilla tors with different natural frequencies are investigated by asymptotic and numerical methods. The conditions for the onset and existence of the regime s of global (all-to-all) and cluster (inside several subsets of elements) f requency synchronization are determined. It is found that there exist monos table and multistable regimes of cluster synchronization and the respective "soft'' and ''hard" transitions between the structures consisting of a dif ferent number of clusters. It is revealed that the synchronization is obser ved in a broader range of parameters in a randomly formed array than for re gularly arranged oscillators with the natural frequencies varying monotonic ally along the array. [S1063-651X(98)02012-1].