External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators

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.

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Cited by in corpus (24)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Long Time Evolution of Phase Oscillator Systems
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Phase oscillators with global sinusoidal coupling evolve by Mobius group action
• Stability diagram for the forced Kuramoto model
• Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling
• Continuous versus Discontinuous Transitions in the $D$-Dimensional Generalized Kuramoto Model: Odd $D$ is Different
• Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Non-universal results induced by diversity distribution in coupled excitable systems
• Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
• Generating macroscopic chaos in a network of globally coupled phase oscillators
• Complex macroscopic behavior in systems of phase oscillators with adaptive coupling
• Complexity Reduction Ansatz for Systems of Interacting Orientable Agents: Beyond The Kuramoto Model
• Synchronization scenarios in the Winfree model of coupled oscillators
• Echo Phenomena in Large Systems of Coupled Oscillators
• Driven synchronization in random networks of oscillators
• Synchronization transitions on connectome graphs with external force
• Event--related desynchronization in diffusively coupled oscillator models
• Arnol'd Tongues in Oscillator Systems with Nonuniform Spatial Driving
• Topological phase transition in the periodically forced Kuramoto model
• Basin sizes depend on stable eigenvalues in the Kuramoto model
• Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity
• Stability of entrainment of a continuum of coupled oscillators