Small-world networks of Kuramoto oscillators

DOI10.1016/j.physd.2013.09.008zbMath1286.34076arXiv1307.0798OpenAlexW1968878530MaRDI QIDQ2448677

Georgi S. Medvedev

Publication date: 5 May 2014

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0798

zbMATH Keywords

coupled oscillatorsrandom graphssynchronization

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (26)

Sparse Monte Carlo Method for Nonlocal Diffusion Problems ⋮ The mean field analysis of the Kuramoto model on graphs. I: The mean field equation and transition point formulas ⋮ Convergence and stability of generalized gradient systems by Łojasiewicz inequality with application in continuum Kuramoto model ⋮ Stability and Bifurcation of Mixing in the Kuramoto Model with Inertia ⋮ Consensus and voting on large graphs: an application of graph limit theory ⋮ The mathematics behind chimera states ⋮ Multi-population phase oscillator networks with higher-order interactions ⋮ Adaptive dynamical networks ⋮ Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability, and Bifurcations ⋮ Stability of twisted states in the Kuramoto model on Cayley and random graphs ⋮ Stability of Twisted States in the Continuum Kuramoto Model ⋮ Degeneracy results for fully nonlinear integral operators ⋮ Equilibria in Kuramoto Oscillator Networks: An Algebraic Approach ⋮ Comparison between the deterministic and stochastic models of nonlocal diffusion ⋮ Travelling waves in arrays of delay-coupled phase oscillators ⋮ Topological States in the Kuramoto Model ⋮ The nonlinear heat equation on \(W\)-random graphs ⋮ Random Walks on Dense Graphs and Graphons ⋮ The Kuramoto model on power law graphs: synchronization and contrast states ⋮ Bifurcations in the Kuramoto model on graphs ⋮ Synchronization of Kuramoto oscillators in small-world networks ⋮ High-dimensional Kuramoto model limited on smooth curved surfaces ⋮ Partially coherent twisted states in arrays of coupled phase oscillators ⋮ Power Network Dynamics on Graphons ⋮ Consensus on simplicial complexes: Results on stability and synchronization ⋮ Flow and Elastic Networks on the 𝑛-Torus: Geometry, Analysis, and Computation

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