New Results of Synchronization Condition of the Non-Uniform Kuramoto Oscillators

This paper addresses the synchronization problem of the non-uniform Kuramoto oscillators, i.e., the Kuramoto oscillators with non-homogeneous damping coefficients and coupling strengths. As a solution to this problem, we present a new necessary condition for the synchronization of the n oscillators,...

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Bibliographic Details
Published inChinese Control Conference pp. 247 - 252
Main Authors Shimohashi, Takayuki, Xin, Xin, Izumi, Shinsaku, Yamasaki, Taiga
Format Conference Proceeding
LanguageEnglish
Japanese
Published Technical Committee on Control Theory, Chinese Association of Automation 01.07.2018
Subjects
Couplings
Damping
Frequency synchronization
Numerical simulation
Oscillators
Synchronization
Upper bound
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ISSN1934-1768
DOI10.23919/ChiCC.2018.8484256

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Summary:This paper addresses the synchronization problem of the non-uniform Kuramoto oscillators, i.e., the Kuramoto oscillators with non-homogeneous damping coefficients and coupling strengths. As a solution to this problem, we present a new necessary condition for the synchronization of the n oscillators, and show that it is tighter than an existing necessary condition proposed in Dödier and Bullo (SIAM Journal on Control and Optimization, vol. 50, no. 3, 2012). For the oscillators of cases of n = 3,4, and 5, our numerical simulation investigations of 10000 systems for each case with the parameters generated randomly show that the conservativeness of the existing condition is reduced considerably by our newly presented condition.
ISSN:1934-1768
DOI:10.23919/ChiCC.2018.8484256