This article explores the global stochastic synchronization of the Kuramoto-oscillator networks with duplex topological structures. The initial phase diameter can be arbitrarily large and the coupling gain of the Kuramoto-oscillator networks can be relatively weak. In particular, two different scenarios of the noise diffusion process are introduced, which cover the noise affecting the sinusoidal coupling process in the Kuramoto-oscillator layer and the networked communication in the control layer, respectively. The local and global connectivity criteria, related to the network topologies, coupling strength, and control gains, are derived rigorously to achieve the global stochastic asymptotic phase agreement and frequency synchronization, respectively. Finally, the validity of the theoretical results is verified via numerical simulation, which further shows that phase agreement is robust to noise perturbation, while frequency synchronization is peculiarly sensitive.

This letter addresses the problem of robust global predefined-time synchronization for a class of nonlinear systems, in which the settling-time is explicit compared with the conventional fixed-time synchronization. Specially, the designed control scheme is smooth, namely differentiable, which is distinguished from the traditional fast control methods containing the signum function. By the Lyapunov stability analysis, the sufficient criterion is derived for achieving the global predefined-time synchronization. More importantly, the obtained results have been directly applied into synchronizing two chaotic systems. Finally, the numerical simulation on predefined-time synchronization of chaotic systems is arranged for verifying the correction and effectiveness of theoretical results.