New Results of Synchronization Condition of the Non-Uniform Kuramoto Oscillators - Shimohashi, Takayuki; Xin, Xin; Izumi, Shinsaku; Yamasaki, Taiga (Chinese Control Conference, 2018)
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.