Two-community noisy Kuramoto model with general interaction strengths: Part II

Abstract

We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. Using a geometric interpretation of the self-consistency equations developed in Part I of this series as well as perturbation arguments we are able to identify all solution boundaries in the phase diagram. This allows us to completely classify the phase diagram in the four dimensional parameter space and identify all possible bifurcation points. Furthermore, we analyze the asymptotic behavior of the solution boundaries. To illustrate these results and the rich behavior of the model we present phase diagrams for selected regions of the parameter space.