Two-community noisy Kuramoto model with general interaction strengths: Part II
arXiv:2007.11321 · doi:10.1063/5.0022625
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.
arXiv comment19 pages, 14 figures
References in corpus (9)
- Conformists and contrarians in a Kuramoto model with identical natural frequencies
- Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
- Dynamical aspects of mean field plane rotators and the Kuramoto model
- Connecting the Kuramoto Model and the Chimera State
- Approximate solution to the stochastic Kuramoto model
- Collective mode reductions for populations of coupled noisy oscillators
- Collective dynamics in two populations of noisy oscillators with asymmetric interactions
- Synchronization of phase oscillators on the hierarchical lattice
- Two-community noisy Kuramoto model with general interaction strengths: Part II