Here, the exponential synchronization about mean square problem of two complex dynamical networks with stochastic perturbations is investigated. A novel drive-response complex network model is formulated which is linear coupling with both time-varying delay and non-delay, meanwhile, this model also includes stochastic perturbations of vector-form. Based on the Lyapunov steady theory, stochastic differential equations, and matrix theory, several effective synchronous conditions are obtained to ensure exponential synchronization in mean square of the proposed complex dynamical networks by periodically intermittent pinning. Finally, several numerical simulations are performed to verify the theoretical results and the control methodology.

This paper is concerned with the outer exponential synchronization of the drive‐response complex dynamical networks subject to time‐varying delays. The dynamics of nodes is complex valued, the interactions among of the nodes are directed, and the two coupling matrices in the drive system and the response system are also different. The intermittent pinning control is proposed to achieve outer exponential synchronization in the aperiodical way. Some novel sufficient conditions are derived to guarantee outer exponential synchronization of the considered complex‐valued complex networks by using the Lyapunov functional method. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed control protocols.

A novel linear complex system for hydroturbine‐generator sets in multimachine power systems is suggested in this paper and synchronization of the power‐grid networks is studied. The advanced graph theory and stability theory are combined to solve the problem. Here we derive a sufficient condition under which the synchronous state of power‐grid networks is stable in disturbance attenuation. Finally, numerical simulations are provided to illustrate the effectiveness of the results by the IEEE 39 bus system.

In this paper, the exponentially synchronization in the mean square is investigated for two different stochastic complex networks with hybrid coupling and time-varying delay via pinning control. By utilizing the Lyapunov stability theory, stochastic analysis theory, as well as matrix analysis, the sufficient conditions are derived to guarantee the exponential synchronization for any initial values through a feedback scheme. The numerical simulation is provided to show the effectiveness of the theoretical results.

In this paper, the moment exponential synchronization problems of drive-response stochastic memristor neural networks are studied via a state feedback controller. The dynamics of the memristor neural network are nonidentical, consisting of both asymmetrically nondelayed and delayed coupled, state-dependent, and subject to exogenous stochastic perturbations. The pth moment exponential synchronization of these drive-response stochastic memristor neural networks is guaranteed under some testable and computable sufficient conditions utilizing differential inclusion theory and Filippov regularization. Finally, the correctness and effectiveness of our theoretical results are demonstrated through a numerical example.