Multi-population phase oscillator networks with higher-order interactions

DOI10.1007/s00030-022-00796-xzbMath1506.35235arXiv2012.04943OpenAlexW3113172140MaRDI QIDQ2172752

Christian Kuehn, Christian Bick, Tobias Böhle

Publication date: 16 September 2022

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.04943

zbMATH Keywords

stability analysissynchronizationcharacteristic systemKuramoto modelmean-fieldhigher-order interactions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-ordinary differential equations (45J05) Integro-partial differential equations (45K05) Population dynamics (general) (92D25) Asymptotics of solutions to integral equations (45M05) Stability theory for integral equations (45M10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Vlasov equations (35Q83) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84)

Related Items (3)

Chimera dynamics of generalized Kuramoto–Sakaguchi oscillators in two-population networks ⋮ Mean-field coupled systems and self-consistent transfer operators: a review ⋮ The structure and dynamics of networks with higher order interactions

Cites Work

• Unnamed Item
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Dynamics of heterogeneous oscillator ensembles in terms of collective variables
• Contractivity of transport distances for the kinetic Kuramoto equation
• Chemical oscillations, waves, and turbulence
• Networks beyond pairwise interactions: structure and dynamics
• On the complete phase synchronization for the Kuramoto model in the mean-field limit
• Constants of motion for superconducting Josephson arrays
• The dynamics of \(n\) weakly coupled identical oscillators
• From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Heteroclinic dynamics of localized frequency synchrony: heteroclinic cycles for small populations
• Heteroclinic dynamics of localized frequency synchrony: stability of heteroclinic cycles and networks
• Synchronization analysis of Kuramoto oscillators
• Small-world networks of Kuramoto oscillators
• Markov-Komposition und eine Anwendung auf Martingale. (Markov compositions and an application to martingales)
• The Nonlinear Heat Equation on Dense Graphs and Graph Limits
• On the Vlasov Limit for Systems of Nonlinearly Coupled Oscillators without Noise
• Community structure in social and biological networks
• The Mean Field Equation for the Kuramoto Model on Graph Sequences with Non-Lipschitz Limit
• State-dependent effective interactions in oscillator networks through coupling functions with dead zones
• Graphop Mean-Field Limits for Kuramoto-Type Models
• Action convergence of operators and graphs
• Power Network Dynamics on Graphons
• The mathematics of asymptotic stability in the Kuramoto model
• Wahrscheinlichkeitstheorie

This page was built for publication: Multi-population phase oscillator networks with higher-order interactions