Impulsive mean square exponential synchronization of stochastic dynamical networks with hybrid time-varying delays

This paper investigates the mean square exponential synchronization problem for complex dynamical networks with stochastic disturbances and hybrid time-varying delays, both internal delay and coupling delay are considered in the model. At the same time, the coupled time-delay is also probabilistic in two time interval. Impulsive control method is applied to force all nodes synchronize to a chaotic orbit, and impulsive input delay is also taken into account. Based on the theory of stochastic differential equation, an impulsive differential inequality and some analysis techniques, several simple and useful criteria are derived to ensure mean square exponential synchronization of the stochastic dynamical networks. Furthermore, pinning impulsive strategy is studied. An effective method is introduced to select the controlled nodes at each impulsive constants. Numerical simulations are exploited to demonstrate the effectiveness of the theory results in this paper

IEEE Access Special Section Editorial: Recent Advances on Hybrid Complex Networks: Analysis and Control

Complex networks typically involve multiple disciplines due to network dynamics and their statistical nature. When modeling practical networks, both impulsive effects and logical dynamics have recently attracted increasing attention. Hence, it is of interest and importance to consider hybrid complex networks with impulsive effects and logical dynamics. Relevant research is prevalent in cells, ecology, social systems, and communication engineering. In hybrid complex networks, numerous nodes are coupled through networks and their properties usually lead to complex dynamic behaviors, including discrete and continuous dynamics with finite values of time and state space. Generally, continuous and discrete sections of the systems are described by differential and difference equations, respectively. Logical networks are used to model the systems where time and state space take finite values. Although interesting results have been reported regarding hybrid complex networks, the analysis methods and relevant results could be further improved with respect to conservative impulsive delay inequalities and reproducibility of corresponding stability or synchronization criteria. Therefore, it is necessary to devise effective approaches to improve the analysis method and results dealing with hybrid complex networks

Exponential stabilization of fractional-order continuous-time dynamic systems via event-triggered impulsive control

Exponential stabilization of fractional-order continuous-time dynamic systems via eventtriggered impulsive control (EIC) approach is investigated in this paper. Nonlinear and linear fractional-order continuous-time dynamic systems are studied, respectively. The impulsive instants are determined by some given event-triggering function and event-triggering condition, which are dependent on the state of the systems. Sufficient conditions on exponential stabilization for nonlinear and linear cases are presented, respectively. Moreover, the Zeno-behavior of impulsive instants is excluded. Finally, the validity of theoretical results are also illustrated by some numerical simulation examples including the synchronization control of fractional-order jerk chaotic system

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results