The emergence of coherence in complex networks of heterogeneous dynamical systems

Abstract

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength, all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.

arXiv comment4 pages, 1 figure. Published version

References in corpus (9)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• The onset of synchronization in large networks of coupled oscillators
• Synchronization of Kuramoto Oscillators in Scale-Free Networks
• Frequency synchronization in random oscillator network
• Synchronization transition in scale-free networks: Clusters of synchrony
• Synchronization in large directed networks of coupled phase oscillators
• The Onset of Synchronization in Systems of Globally Coupled Chaotic and Periodic Oscillators
• Path-integral approach to the dynamics in sparse random network

Cited by in corpus (20)

• Spontaneous synchrony in power-grid networks
• Approximating the largest eigenvalue of network adjacency matrices
• Approximating Spectral Impact of Structural Perturbations in Large Networks
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Partially Locked States in Coupled Oscillators due to Inhomogeneous Coupling
• Connectivity-Driven Coherence in Complex Networks
• Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function
• Isochronal synchronization of delay-coupled systems
• Network-complement transitions, symmetries, and cluster synchronization
• Optimization of synchronizability in multiplex networks
• Complex Network Approach to Fractional Time Series
• Sensitive Dependence of Optimal Network Dynamics on Network Structure
• Network connectivity during mergers and growth: optimizing the addition of a module
• Approximating the Largest Eigenvalue of the Modified Adjacency Matrix of Networks with Heterogeneous Node Biases
• Social Climber attachment in forming networks produces phase transition in a measure of connectivity
• Graphop Mean-Field Limits and Synchronization for the Stochastic Kuramoto Model
• Sample-to-sample fluctuations in real-network ensembles
• Quantifying the dynamics of coupled networks of switches and oscillators
• Network Extreme Eigenvalue - from Multimodal to Scale-free Network
• The spark of synchronization in heterogeneous networks of chaotic maps