Cluster Synchrony in Systems of Coupled Phase Oscillators with Higher-Order Coupling

Abstract

We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the dynamics in the limit of a large number of oscillators and use it to quantify the degree of cluster synchrony, cluster asymmetry, and switching. We use a variation of the recent dimensionality-reduction technique of Ott and Antonsen [Chaos {\bf 18}, 037113 (2008)] and find an analytic description of the degree of cluster synchrony valid on a globally attracting manifold. Shaped by this manifold, there is an infinite family of steady-state distributions of oscillators, resulting in a high degree of multi-stability in the cluster asymmetry. We also show how through external forcing the degree of asymmetry can be controlled, and suggest that systems displaying cluster synchrony can be used to encode and store data.

9 pages, 9 figures

References in corpus (12)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Chimera states in heterogeneous networks
• Stability diagram for the forced Kuramoto model
• Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
• External Periodic Driving of Large Systems of Globally Coupled Phase Oscillators
• Noise-Induced Synchronization of a Large Population of Globally Coupled Nonidentical Oscillators
• Invariant submanifold for series arrays of Josephson junctions
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• Low Dimensional Description of Pedestrian-Induced Oscillation of the Millennium Bridge
• Synchronization and clustering of synthetic genetic networks: A role for cis-regulatory modules

Cited by in corpus (42)

• The Kuramoto model in complex networks
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Glassy states and superrelaxation in populations of coupled phase oscillators
• Erosion of synchronization in networks of coupled oscillators
• Noise-Induced Synchronization, Desynchronization, and Clustering in Globally Coupled Nonidentical Oscillators
• Bifurcation analysis and structural stability of simplicial oscillator populations
• Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling
• Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
• Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions
• The Kuramoto model of coupled oscillators with a bi-harmonic coupling function
• Complex macroscopic behavior in systems of phase oscillators with adaptive coupling
• Low-Dimensional Dynamics for Higher Order Harmonic Globally Coupled Phase Oscillator Ensemble
• Analysis of cluster explosive synchronization in complex networks
• Self-sustained irregular activity in an ensemble of neural oscillators
• Higher-order interactions induce anomalous transitions to synchrony
• Identifying symmetries and predicting cluster synchronization in complex networks
• Frequency assortativity can induce chaos in oscillator networks
• Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling
• Memory selection and information switching in oscillator networks with higher-order interactions
• Optimal synchronization of directed complex networks
• Multistability in coupled oscillator systems with higher-order interactions and community structure
• Low Dimensional Dynamics of the Kuramoto Model with Rational Frequency Distributions
• Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates
• Collective dynamics on higher-order networks
• Dynamical equivalence between Kuramoto models with first- and higher-order coupling
• Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions
• Dynamics of two populations of phase oscillators with different frequency distributions
• Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays
• Erosion of synchronization: Coupling heterogeneity and network structure
• Symmetry and symmetry breaking in coupled oscillator communities
• Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies
• Irregular collective dynamics in a Kuramoto-Daido system
• Locating line and node disturbances in networks of diffusively coupled dynamical agents
• Cluster Synchronization via Graph Laplacian Eigenvectors
• An entropy based clustering order parameter for finite ensembles of oscillators
• Collective dynamics of identical phase oscillators with high-order coupling
• Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators
• Comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"