The Kuramoto model on power law graphs: synchronization and contrast states

DOI10.1007/s00332-018-9489-3zbMath1466.37069OpenAlexW2891902476MaRDI QIDQ2022736

Xuezhi Tang, Georgi S. Medvedev

Publication date: 29 April 2021

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-018-9489-3

zbMATH Keywords

coupled oscillatorssynchronizationmean field limitgraph limitscale-free graphchimera state

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Approximation methods and numerical treatment of dynamical systems (37M99) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Synchronization of solutions to ordinary differential equations (34D06)

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Cites Work

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• Limits of randomly grown graph sequences
• Limits of dense graph sequences
• Dynamical systems on networks. A tutorial
• Stability of twisted states in the Kuramoto model on Cayley and random graphs
• Weakly connected neural networks
• Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford
• The mean field analysis of the Kuramoto model on graphs. I: The mean field equation and transition point formulas
• The mean field analysis of the Kuramoto model on graphs. II: Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations
• Small-world networks of Kuramoto oscillators
• The nonlinear heat equation on \(W\)-random graphs
• Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators
• Heterophilious Dynamics Enhances Consensus
• Stability of Twisted States in the Continuum Kuramoto Model
• Emergence of Scaling in Random Networks
• Stochastic Stability of Continuous Time Consensus Protocols
• On the Vlasov Limit for Systems of Nonlinearly Coupled Oscillators without Noise
• The size of the sync basin
• The Mean Field Equation for the Kuramoto Model on Graph Sequences with Non-Lipschitz Limit
• Bifurcations in the Kuramoto model on graphs
• Real Analysis and Probability
• An 𝐿^{𝑝} theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions
• Low dimensional behavior of large systems of globally coupled oscillators
• Chimera states in heterogeneous networks
• A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model
• Center manifold reduction for large populations of globally coupled phase oscillators
• The average distances in random graphs with given expected degrees
• CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS
• The Semilinear Heat Equation on Sparse Random Graphs