Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization

DOI10.1063/1.4907952zbMath1345.34053OpenAlexW2139319800WikidataQ50953754 ScholiaQ50953754MaRDI QIDQ2821608

Eduardo A. Canale, Pablo Monzón

Publication date: 21 September 2016

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

Full work available at URL: https://semanticscholar.org/paper/57c0f093a0b59c202a8c8a29fd1cb69061164f2c

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Graph operations (line graphs, products, etc.) (05C76) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (5)

High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally ⋮ The Kuramoto model on dynamic random graphs ⋮ Dense networks that do not synchronize and sparse ones that do ⋮ The lower bound of the network connectivity guaranteeing in-phase synchronization ⋮ Sufficiently dense Kuramoto networks are globally synchronizing

Cites Work

• Synchronization in complex networks of phase oscillators: a survey
• Invitation to topological robotics
• Applications of centre manifold theory
• Constants of motion for superconducting Josephson arrays
• There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model
• The size of the sync basin
• Local implications of almost global stability
• Convergence of the Iterates of Descent Methods for Analytic Cost Functions
• A dual to Lyapunov's stability theorem
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