Feedback-induced desynchronization and oscillation quenching in a population of globally coupled oscillators

Abstract

Motivated from a wide range of applications, various methods to control synchronization in coupled oscillators have been proposed. Previous studies have demonstrated that global feedback typically induces three macroscopic behaviors: synchronization, desynchronization, and oscillation quenching. However, analyzing all of these transitions within a single theoretical framework is difficult, and thus the feedback effect is only partially understood in each framework. Herein, we analyze a model of globally coupled phase oscillators exposed to global feedback, which shows all of the typical macroscopic dynamical states. Analytical tractability of the model enables us to obtain detailed phase diagrams where transitions and bistabilities between different macroscopic states are identified. Additionally, we propose strategies to steer the oscillators into targeted states with minimal feedback strength. Our study provides a useful overview of the effect of global feedback and is expected to serve as a benchmark when more sophisticated feedback needs to be designed.

arXiv comment34 pages, 8 figures

References in corpus (14)

• Synchronization in complex networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Spontaneous synchrony in power-grid networks
• Long Time Evolution of Phase Oscillator Systems
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Stability diagram for the forced Kuramoto model
• Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
• Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
• Decentralised control of material or traffic flows in networks using phase-synchronisation
• Synchronization Engineering: Theoretical Framework and Application to Dynamical Clustering
• Structure of Cell Networks Critically Determines Oscillation Regularity
• Clustering in Globally Coupled Oscillators Near a Hopf Bifurcation: Theory and Experiments
• Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback

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