Continuum limits of coupled oscillator networks depending on multiple sparse graphs

DOI10.1007/s00332-023-09921-1zbMath1521.34036arXiv2305.16728OpenAlexW4379142443MaRDI QIDQ6174593

Kazuyuki Yagasaki, Ryosuke Ihara

Publication date: 14 July 2023

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

Full work available at URL: https://arxiv.org/abs/2305.16728

zbMATH Keywords

continuum limitrandom graphcoupled oscillator networksparse graph

Mathematics Subject Classification ID

Applications of graph theory (05C90) Integro-partial differential equations (45K05) Stability of solutions to ordinary differential equations (34D20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary lattice differential equations (34A33)

Cites Work

• Chemical oscillations, waves, and turbulence
• The mean field analysis of the Kuramoto model on graphs. I: The mean field equation and transition point formulas
• On input-to-state stability for stochastic coupled control systems on networks
• The geometry of spontaneous spiking in neuronal networks
• The continuum limit of the Kuramoto model on sparse random graphs
• The mean field analysis of the Kuramoto model on graphs. II: Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations
• The nonlinear heat equation on \(W\)-random graphs
• On convergence and growth of partial sums of Fourier series
• Stationary Bumps in Networks of Spiking Neurons
• Multistability of twisted states in non-locally coupled Kuramoto-type models
• Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators
• The Nonlinear Heat Equation on Dense Graphs and Graph Limits
• Stochastic Stability of Continuous Time Consensus Protocols
• The size of the sync basin
• On controlling networks of limit-cycle oscillators
• Bifurcations in the Kuramoto model on graphs
• On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
• Consensus dynamics on weighted multiplex networks: a long-range interaction perspective
• Low dimensional behavior of large systems of globally coupled oscillators
• 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
• Collective dynamics of ‘small-world’ networks
• CHIMERA STATES IN A RING OF NONLOCALLY COUPLED OSCILLATORS
• The Semilinear Heat Equation on Sparse Random Graphs
• Graphon Control of Large-Scale Networks of Linear Systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item