A mean-field limit of the Lohe matrix model and emergent dynamics

DOI10.1007/s00205-019-01416-2zbMath1425.37046arXiv1809.05086OpenAlexW3104022259MaRDI QIDQ2326463

Seung-Yeal Ha, François Golse

Publication date: 7 October 2019

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.05086

zbMATH Keywords

Schrödinger equationcollective dynamicsKuramoto modelVlasov-type equation

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Vlasov equations (35Q83) PDEs in connection with statistical mechanics (35Q82)

Related Items (9)

Uniform stability and emergent dynamics of particle and kinetic Lohe matrix models ⋮ Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies ⋮ Heterogeneous gradient flows in the topology of fibered optimal transport ⋮ State-Dependent Dynamics of the Lohe Matrix Ensemble on the Unitary Group under the Gradient Flow ⋮ Stochastic Lohe matrix model on the Lie group and mean-field limit ⋮ Cluster Synchrony of High-Dimensional Kuramoto Models with Higher-Order Couplings ⋮ Emergent dynamics of the Lohe matrix ensemble on a network under time-delayed interactions ⋮ Emergent behavior of a second-order Lohe matrix model on the unitary group ⋮ Mean-field limit for particle systems with topological interactions

Cites Work

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• On the mean field and classical limits of quantum mechanics
• On the emergence and orbital stability of phase-locked states for the Lohe model
• Emergence of phase-locked states for the Kuramoto model in a large coupling regime
• Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
• Synchronization in complex networks of phase oscillators: a survey
• Collective synchronization of classical and quantum oscillators
• The Schrödinger equation in the mean-field and semiclassical regime
• Chemical oscillations, waves, and turbulence
• Bifurctions, patterns and symmetry. Selected papers dedicated to the memory of John David Crawford
• Synchronization and stability for quantum Kuramoto
• On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds
• High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally
• Emergent dynamics of a generalized Lohe model on some class of Lie groups
• Synchronization analysis of Kuramoto oscillators
• The spectrum of the locked state for the Kuramoto model of coupled oscillators
• The spectrum of the partially locked state for the Kuramoto model
• Complete Entrainment of Lohe Oscillators under Attractive and Repulsive Couplings
• Practical quantum synchronization for the Schrödinger–Lohe system
• Quantum synchronization over quantum networks
• Global Phase-Locking in Finite Populations of Phase-Coupled Oscillators
• On Computing the Critical Coupling Coefficient for the Kuramoto Model on a Complete Bipartite Graph
• Non-Abelian Kuramoto models and synchronization
• Synchronization of relativistic particles in the hyperbolic Kuramoto model
• Synchronization on Riemannian Manifolds: Multiply Connected Implies Multistable
• On Exponential Synchronization of Kuramoto Oscillators
• On the Critical Coupling for Kuramoto Oscillators

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