Fixed-time stochastic synchronization of Kuramoto oscillators subjected to noisy diffusion process

Abstract

This investigation concerns the phase agreement (PA) for identical Kuramoto oscillators and frequency synchronization (FS) for nonidentical oscillators within fixed-time (FxT) in noisy environments. Comparing with the conventional FxT controllers, this investigation picks the smooth control protocol for stripping the signum function out, which could improve the synchronizing performance of networked systems. Furthermore, due to the ubiquity of stochastic perturbation, this investigation takes the noise into consideration. Additionally, the synchronizing criteria are deduced for realizing the FxT phase-FS in probability, and meanwhile the time estimation (TE) of realizing synchronization is given. At last, simulation results not only validate the correction of theoretical analysis, but also indicate that PA is more robust to stochastic disturbance, whereas FS of oscillators is relatively sensitive.