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

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. By developing a geometric interpretation of the self-consistency equations, we are able to separate the parameter space into ten regions in which we identify the maximum number of solutions in the steady state. Furthermore, we prove that in the steady-state only the angles 0 and $\pi$ are possible between the average phases of the two communities and derive the solution boundary for the unsynchronized solution. Lastly, we identify the equivalence class relation in the parameter space corresponding to the symmetrically synchronized solution.

arXiv comment16 pages 4 figures

References in corpus (18)

• Emergent complex neural dynamics
• Solvable model for chimera states of coupled oscillators
• Synchronization of two interacting populations of oscillators
• Conformists and contrarians in a Kuramoto model with identical natural frequencies
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• 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
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• Collective mode reductions for populations of coupled noisy oscillators
• Collective dynamics in two populations of noisy oscillators with asymmetric interactions
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case
• Asymmetry--induced effects in coupled phase oscillator ensembles: Routes to synchronization
• Routes to synchrony between asymmetrically interacting oscillator ensembles
• Uncovering functional brain signature via random matrix theory
• Synchronization of phase oscillators on the hierarchical lattice
• Two-community noisy Kuramoto model with general interaction strengths: Part I

Cited by in corpus (1)

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