Emergence of local synchronization in an ensemble of heterogeneous Kuramoto oscillators (Q515175)

The authors consider two groups of generalised Kuramoto oscillators. Specifically, there are two groups of phase oscillators, each group having identical local (i.e.,~uncoupled) dynamics, but different local dynamics for the two groups. The within group coupling is all-to-all through sines of phase differences, as is the between group coupling. Much of the paper concerns the conditions under which local exponential synchronization occurs. In this form of synchronization, all phases in one group tend to a common value as \(t\rightarrow\infty\), as do the phases in the other group, but the two groups do not have the same final phases. They also consider ``practical synchronization'' in which the maximum difference in phases over the whole ensemble is uniformly bounded by some constant inversely proportional to the coupling strength. They generalise their results to more than two groups and also provide numerical results to confirm their analyses.