Synchronization of relativistic particles in the hyperbolic Kuramoto model

DOI10.1063/1.5021701zbMath1391.34070OpenAlexW2804252770WikidataQ88952883 ScholiaQ88952883MaRDI QIDQ4575494

Anthony G. Williams, M. A. Lohe, Louis M. Ritchie

Publication date: 13 July 2018

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

Full work available at URL: https://doi.org/10.1063/1.5021701

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Synchronization of solutions to ordinary differential equations (34D06)

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Cites Work

• Unnamed Item
• On the emergence and orbital stability of phase-locked states for the Lohe model
• Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
• Synchronization in complex networks of phase oscillators: a survey
• Synchronization control in networks with uniform and distributed phase lag
• The Kuramoto model in complex networks
• Frequency synchronization and phase agreement in Kuramoto oscillator networks with delays
• Complex networks: structure and dynamics
• Emergent dynamics of a generalized Lohe model on some class of Lie groups
• Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators
• The spectrum of the locked state for the Kuramoto model of coupled oscillators
• Time-delayed interactions and synchronization of identical Lohe oscillators
• Ordinary Differential Equations: Basics and Beyond
• Synchronization of oscillators in a Kuramoto-type model with generic coupling
• Complete Entrainment of Lohe Oscillators under Attractive and Repulsive Couplings
• Large-time dynamics of the asymptotic Lohe model with a small time-delay
• Non-Abelian Kuramoto models and synchronization
• Dynamics of globally coupled oscillators: Progress and perspectives
• Existence of Partial Entrainment and Stability of Phase Locking Behavior of Coupled Oscillators
• Emergent behaviors of a holonomic particle system on a sphere