Topological States in the Kuramoto Model

DOI10.1137/17M112484XzbMath1382.05070arXiv1704.02294OpenAlexW2963295451MaRDI QIDQ4608090

Timothy Ferguson

Publication date: 15 March 2018

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.02294

zbMATH Keywords

fixed pointsgraph topologyKuramoto modelWeyl asymptotic

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Planar graphs; geometric and topological aspects of graph theory (05C10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (7)

Configurational stability for the Kuramoto–Sakaguchi model ⋮ When is sync globally stable in sparse networks of identical Kuramoto oscillators? ⋮ Synchronization and stability for quantum Kuramoto ⋮ A matrix-valued Kuramoto model ⋮ Synchronisation conditions in the Kuramoto model and their relationship to seminorms ⋮ Consensus on simplicial complexes: Results on stability and synchronization ⋮ Flow and Elastic Networks on the 𝑛-Torus: Geometry, Analysis, and Computation

Cites Work

• Unnamed Item
• Unnamed Item
• Chemical oscillations, waves, and turbulence
• Stability of twisted states in the Kuramoto model on Cayley and random graphs
• From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
• Small-world networks of Kuramoto oscillators
• Multistability of twisted states in non-locally coupled Kuramoto-type models
• Multistability of phase-locking and topological winding numbers in locally coupled Kuramoto models on single-loop networks
• Stability of Twisted States in the Continuum Kuramoto Model
• Multistability of phase-locking in equal-frequency Kuramoto models on planar graphs
• There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model
• The size of the sync basin
• Graph Homology and Stability of Coupled Oscillator Networks

This page was built for publication: Topological States in the Kuramoto Model