State-Dependent Dynamics of the Lohe Matrix Ensemble on the Unitary Group under the Gradient Flow

DOI10.1137/19M1294605zbMath1443.34035OpenAlexW3022243076MaRDI QIDQ5109378

Dohyun Kim

Publication date: 11 May 2020

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1294605

zbMATH Keywords

synchronizationadaptive dynamicsKuramoto modelLohe matrix model

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Ordinary differential equations and systems on manifolds (34C40) Synchronization of solutions to ordinary differential equations (34D06)

Related Items (3)

Slow and finite-time relaxations to \(m\)-bipartite consensus on the Stiefel manifold ⋮ Emergent behaviors of Lohe Hermitian sphere particles under time-delayed interactions ⋮ Asymptotic interplay of states and adaptive coupling gains in the Lohe Hermitian sphere model

Cites Work

• Unnamed Item
• Unnamed Item
• On the emergence and orbital stability of phase-locked states for the Lohe model
• First-order aggregation models and zero inertia limits
• Chemical oscillations, waves, and turbulence
• Generalising the Kuramoto model for the study of neuronal synchronisation in the brain
• Enskog-like kinetic models for vehicular traffic
• Behavioral crowds: modeling and Monte Carlo simulations toward validation
• Synchronization and stability for quantum Kuramoto
• On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds
• Asymptotic behavior of gradient flows on the unit sphere with various potentials
• A matrix-valued Kuramoto model
• Emergent behavior of a second-order Lohe matrix model on the unitary group
• Emergence of aggregation in the swarm sphere model with adaptive coupling laws
• A mean-field limit of the Lohe matrix model and emergent dynamics
• Emergent dynamics of a generalized Lohe model on some class of Lie groups
• An adaptive model for synchrony in the firefly Pteroptyx malaccae
• Plasticity and learning in a network of coupled phase oscillators
• Dynamical system approach to synchronization of the coupled Schrödinger–Lohe system
• Reaching a Quantum Consensus: Master Equations that Generate Symmetrization and Synchronization
• Quantum synchronization over quantum networks
• On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives
• Emergent Dynamics of Kuramoto Oscillators with Adaptive Couplings: Conservation Law and Fast Learning
• Non-Abelian Kuramoto models and synchronization
• A kinetic model of vehicular traffic and its associated bimodal equilibrium solutions
• The stability of fixed points for a Kuramoto model with Hebbian interactions
• Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
• Hierarchical frequency clusters in adaptive networks of phase oscillators
• Emergent dynamics of the Lohe matrix ensemble on a network under time-delayed interactions
• Quantum synchronization of two Van der Pol oscillators

This page was built for publication: State-Dependent Dynamics of the Lohe Matrix Ensemble on the Unitary Group under the Gradient Flow