Asymptotic Stability of the Phase-homogeneous Solution to the Kuramoto--Sakaguchi Equation with Inertia

DOI10.1137/20M1368719zbMath1472.35387arXiv1806.04953OpenAlexW3168993489MaRDI QIDQ4997164

Seung-Yeal Ha, Young-Pil Choi, Yinglong Zhang, Qing-Hua Xiao

Publication date: 28 June 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04953

zbMATH Keywords

Cauchy problemsynchronizationKuramoto-Sakaguchi equationnonlinear Vlasov-Fokker-Planck equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Vlasov equations (35Q83) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Fokker-Planck equations (35Q84)

Related Items (3)

Cardinality of Collisions in Asymptotic Phase-Locking for the Kuramoto Model with Inertia ⋮ A Diffusion Limit for the Parabolic Kuramoto--Sakaguchi Equation with Inertia ⋮ On the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena

Cites Work

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• Stability and bifurcation for the Kuramoto 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
• Collective synchronization of classical and quantum oscillators
• Nonlinear instability of the incoherent state for the Kuramoto-Sakaguchi-Fokker-Plank equation
• Complete synchronization of Kuramoto oscillators with finite inertia
• Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-Euler system
• On Landau damping
• A kinetic flocking model with diffusion
• Contractivity of transport distances for the kinetic Kuramoto equation
• On the complete phase synchronization for the Kuramoto model in the mean-field limit
• From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
• Emergent dynamics of the Kuramoto ensemble under the effect of inertia
• The Landau equation in a periodic box
• Emergence of phase concentration for the Kuramoto-Sakaguchi equation
• Coherence stability and effect of random natural frequencies in populations of coupled oscillators
• Remarks on the nonlinear stability of the Kuramoto-Sakaguchi equation
• Self-synchronization of coupled oscillators with hysteretic responses
• Global existence and asymptotic behavior of measure valued solutions to the kinetic Kuramoto-Daido model with inertia
• Landau damping in the Kuramoto model
• An adaptive model for synchrony in the firefly Pteroptyx malaccae
• Uniqueness and well-ordering of emergent phase-locked states for the Kuramoto model with frustration and inertia
• The Navier–Stokes–Vlasov–Fokker–Planck System near Equilibrium
• Global classical solutions of the Vlasov–Fokker–Planck equation with local alignment forces
• Landau Damping to Partially Locked States in the Kuramoto Model
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• The Boltzmann equation in the whole space
• Remarks on the nonlinear stability of the Kuramoto model with inertia
• Landau damping in Sobolev spaces for the Vlasov-HMF model

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