External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators

TL;DR

This paper analyzes the effects of a periodic external drive on large systems of globally coupled phase oscillators, identifying stable states, bifurcations, and phase diagrams through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of stationary states, stability, and bifurcations in driven oscillator systems with all-to-all sine coupling, supported by numerical simulations.

Findings

Identification of stable stationary states under external driving

Construction of phase diagrams showing different system behaviors

Bifurcation analysis delineating transitions between behaviors

Abstract

Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a sinusoidal external drive is considered. The stationary states and their stability are determined. Using the stability information and numerical experiments, parameter space phase diagrams showing when different types of system behavior apply are constructed, and the bifurcations marking transitions between different types of behavior are delineated. The analysis is supported by results of direct numerical simulation of an ensemble of oscillators.