Finite-Time and Fixed-Time Synchronization of Kuramoto-Oscillator Network With Multiplex Control

In this paper, the finite-time and fixed-time synchronization of a generalized Kuramoto model with identical and nonidentical oscillators are investigated, respectively. Given a (weak) coupling strength or initial phases dispersed over a circle, the Kuramoto-oscillator network can achieve phase-frequency synchronization within a finite time, and the upper bound of synchronization time can be estimated. Compared with the finite-time synchronization where the convergence rate relies on the initial conditions, the settling time of fixed-time synchronization can be adjusted to desired values in advance regardless of initial configurations. Deploying a novel multiplex control, the local and global connectivity conditions for realizing finite-time and fixed-time phase-frequency synchronization are derived successively based on the Lyapunov stability theory, and numerical examples verify their effectiveness and feasibility.