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TITLE Emergent behaviors of the continuum thermodynamic Kuramoto model in a large coupling regime
KIAS AUTHORS Ha, Seung-Yeal
JOURNAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2021
ARCHIVE  
ABSTRACT We study the emergent dynamics of the continuum thermodynamic Kuramoto model which arises from the continuum limit of the lattice thermodynamic Kuramoto (TK) model [17]. The continuum TK model governs the time-evolution of the Kuramoto phase field in a temperature field, and the solution to the lattice TK model corresponds to the simple function-valued solution to the continuum TK model on a compact spatial region. Asymptotic emergent estimates for the continuum TK model consist of two sequential processes (temperature homogenization and phase-locking). First, we show that the temperature field relaxes to a positive constant temperature exponentially fast pointwise depending on the nature of the communication weight function. In contrast, the emergent dynamics of phase field exhibits a more rich phenomena. For the phase field in a constant natural frequency field, the phase field concentrates to either one-point cluster or bipolar cluster, whereas in a nonconstant natural frequency field, the phase field exhibits a phased-locked state asymptotically. We also provide several numerical simulations and compare them with analytical results. (c) 2021 Elsevier Inc. All rights reserved.
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