The effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph

Abstract

We have extended the study of the Kuramoto model with additive Gaussian noise running on the KKI-18 large human connectome graph. We determined the dynamical behavior of this model by solving it numerically in an assumed homeostatic state, below the synchronization crossover point we determined previously. The de-synchronization duration distributions exhibit power-law tails, characterized by the exponent in the range $1.1<{\tau }_t<2$, overlapping the in vivo human brain activity experiments by Palva et al. We show that these scaling results remain valid, by a transformation of the ultra-slow eigen-frequencies to Gaussian with unit variance. We also compare the connectome results with those, obtained on a regular cube with $N=10^6$ nodes, related to the embedding space, and show that the quenched internal frequencies themselves can cause frustrated synchronization scaling in an extended coupling space.

arXiv comment26 pages, 11 figures, accepted version in J. Neuroscience

References in corpus (23)

• From Louvain to Leiden: guaranteeing well-connected communities
• Critical Phenomena and Renormalization-Group Theory
• Chimera States for Coupled Oscillators
• Optimal Dynamical Range of Excitable Networks at Criticality
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Griffiths phases and the stretching of criticality in brain networks
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization
• Predicting criticality and dynamic range in complex networks: effects of topology
• Optimal hierarchical modular topologies for producing limited sustained activation of neural networks
• Frustrated hierarchical synchronization and emergent complexity in the human connectome network
• Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs
• Homeostatic plasticity and emergence of functional networks in a whole-brain model at criticality
• Griffiths phases and localization in hierarchical modular networks
• The topology of large Open Connectome networks for the human brain
• On the equivalence of phase-oscillator and integrate-and-fire models
• Heterogeneity effects in power-grid network models
• MIGRAINE: MRI Graph Reliability Analysis and Inference for Connectomics
• Robust short-term memory without synaptic learning
• Critical dynamics on a large human Open Connectome network
• Slow, bursty dynamics as the consequence of quenched network topologies
• Dynamic critical behaviors of three-dimensional XY models related to superconductors/superfluids

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• Synchronization transitions on connectome graphs with external force
• Chimera states in neural networks and power systems
• Synchronization transition of the second-order Kuramoto model on lattices
• Modelling on the very large-scale connectome
• Synchronization on star graph with noise
• Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions