TY - JOUR

T1 - Exponential synchronization of finite-dimensional kuramoto model at critical coupling strength

AU - Choi, Young Pil

AU - Ha, Seung Yeal

AU - Kang, Myeongmin

AU - Kang, Myungjoo

PY - 2013

Y1 - 2013

N2 - We discuss the exponential synchronization for an ensemble of Kuramoto oscillators at the critical coupling strength, which is the diameter of the set consisting of natural frequencies. When the number of distinct natural frequencies is greater than two and the initial phases are strictly confined in an interval of length π/2, we show that the initial configuration evolves toward a phase-locked state at least exponentially fast. This fast convergence toward the phase-locked state is markedly different from an ensemble of Kuramoto oscillators with only two distinct natural frequencies. For this, we derive a Gronwall inequality for the frequency diameter to obtain complete synchronization. We also compare our analytical results with numerical simulation results.

AB - We discuss the exponential synchronization for an ensemble of Kuramoto oscillators at the critical coupling strength, which is the diameter of the set consisting of natural frequencies. When the number of distinct natural frequencies is greater than two and the initial phases are strictly confined in an interval of length π/2, we show that the initial configuration evolves toward a phase-locked state at least exponentially fast. This fast convergence toward the phase-locked state is markedly different from an ensemble of Kuramoto oscillators with only two distinct natural frequencies. For this, we derive a Gronwall inequality for the frequency diameter to obtain complete synchronization. We also compare our analytical results with numerical simulation results.

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U2 - 10.4310/CMS.2013.v11.n2.a3

DO - 10.4310/CMS.2013.v11.n2.a3

M3 - Article

AN - SCOPUS:84875170193

SN - 1539-6746

VL - 11

SP - 385

EP - 401

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

IS - 2

ER -