Coupled networks and networks with bimodal frequency distributions are equivalent

Abstract

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled, symmetric (sub)populations with unimodal frequency distributions and show that the resulting synchronization patterns may resemble those of a single population with bimodally distributed frequencies. Our proof of the equivalence of their stability, dynamics, and bifurcations, is based on an Ott-Antonsen ansatz. The generalization to networks consisting of multiple (sub)populations vis-à-vis networks with multimodal frequency distributions, however, appears impossible.

4 pages, 4 figures, 1 supplementary pdf file

References in corpus (8)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Chimera states in heterogeneous networks
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• Chimera states in two populations with heterogeneous phase-lag
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• Ott-Antonsen attractiveness for parameter-dependent oscillatory networks

Cited by in corpus (12)

• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Kuramoto model for excitation-inhibition-based oscillations
• Synchronization scenarios in the Winfree model of coupled oscillators
• First-order phase transitions in the Kuramoto model with compact bimodal frequency distributions
• Complex dynamics in adaptive phase oscillator networks
• Multifaceted dynamics of Janus oscillator networks
• Symmetry and symmetry breaking in coupled oscillator communities
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Chaotic Chimera Attractors in a Triangular Network of Identical Oscillators
• A Two-Frequency-Two-Coupling model of coupled oscillators
• Complexity and irreducibility of dynamics on networks of networks
• Competitive Suppression of Synchronization and Non-Monotonic Transitions in Oscillator Communities with Distributed Time Delay