Stability of twisted states in the Kuramoto model on Cayley and random graphs

DOI10.1007/s00332-015-9252-yzbMath1337.34042arXiv1407.3990OpenAlexW3098083269MaRDI QIDQ897155

Georgi S. Medvedev, Xuezhi Tang

Publication date: 17 December 2015

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

Full work available at URL: https://arxiv.org/abs/1407.3990

zbMATH Keywords

Cayley graphPaley graphsynchronizationquasirandom graphKuramoto modeltwisted state

Mathematics Subject Classification ID

Applications of graph theory (05C90) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical systems involving smooth mappings and diffeomorphisms (37C05) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (16)

Sparse Monte Carlo Method for Nonlocal Diffusion Problems ⋮ When is sync globally stable in sparse networks of identical Kuramoto oscillators? ⋮ Consensus and voting on large graphs: an application of graph limit theory ⋮ The mathematics behind chimera states ⋮ Sparse network optimization for synchronization ⋮ Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability, and Bifurcations ⋮ Stability of Twisted States in the Continuum Kuramoto Model ⋮ Comparison between the deterministic and stochastic models of nonlocal diffusion ⋮ Topological States in the Kuramoto Model ⋮ Synchronization of Kuramoto oscillators in dense networks ⋮ The Kuramoto model on power law graphs: synchronization and contrast states ⋮ Bifurcations in the Kuramoto model on graphs ⋮ A matrix-valued Kuramoto model ⋮ On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization ⋮ Emergence of Balance from a Model of Social Dynamics ⋮ Flow and Elastic Networks on the 𝑛-Torus: Geometry, Analysis, and Computation

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