Exponential synchronization of complex networks with finite distributed delays coupling

Fixed-Time Stochastic Synchronization of Complex Networks via Continuous Control

This paper investigates the fixed-time synchronization (FDTS) of complex networks with stochastic perturbations. A new control scheme is designed to realize the synchronization goal. Moreover, the designed controller without sign function is continuous, which means the chattering phenomenon in some previous results can be avoided. By constructing Lyapunov functionals, using the properties of the Weiner process as well as applying a designed comparison system, several FDTS criteria are obtained. Synchronization criteria of this paper are very general and can be utilized in directed and undirected weighted networks. Numerical simulations are given to illustrate the theoretical results.

Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach

This paper is concerned with the synchronization control problem for a class of discrete time-delay complex dynamical networks under a dynamic event-triggered mechanism. For the efficiency of energy utilization, we make the first attempt to introduce a dynamic event-triggering strategy into the design of synchronization controllers for complex dynamical networks. A new discrete-time version of the dynamic event-triggering mechanism is proposed in terms of the absolute errors between control input updates. By constructing an appropriate Lyapunov functional, the dynamics of each network node combined with the introduced event-triggering mechanism are first analyzed, and a sufficient condition is then provided under which the synchronization error dynamics is exponentially ultimately bounded. Subsequently, a set of the desired synchronization controllers is designed by solving a matrix inequality. Finally, a simulation example is provided to verify the effectiveness of the proposed dynamic event-triggered synchronization control scheme.

Synchronization of linearly coupled networks with delays via aperiodically intermittent pinning control

In this paper, we investigate the exponential synchronization problem for linearly coupled networks with delay by pinning a simple aperiodically intermittent controller. The network topology can be directed. Different from previous works, the intermittent control can be aperiodic. Two types of delay are considered. The first case is that the delay is time-varying and large, and in this case, there is no restriction imposed on the delay and the control (and/or rest) width. The other one is that the delay is small enough so that it is less than the minimum of control width. Different approaches are provided to investigate these two cases, and some criteria are given to realize exponential synchronization. Furthermore, by applying the adaptive approach to the second model, we establish a general adaptive theory for intermittent control, which can be applied not only to networks without time delay, but also to delayed networks, regardless of whether the intermittent control is periodic or aperiodic. Finally, the numerical simulations are given to verify the validness of the theoretical results.

Global synchronization of complex dynamical networks through digital communication with limited data rate

This paper studies the global synchronization of complex dynamical network (CDN) under digital communication with limited bandwidth. To realize the digital communication, the so-called uniform-quantizer-sets are introduced to quantize the states of nodes, which are then encoded and decoded by newly designed encoders and decoders. To meet the requirement of the bandwidth constraint, a scaling function is utilized to guarantee the quantizers having bounded inputs and thus achieving bounded real-time quantization levels. Moreover, a new type of vector norm is introduced to simplify the expression of the bandwidth limit. Through mathematical induction, a sufficient condition is derived to ensure global synchronization of the CDNs. The lower bound on the sum of the real-time quantization levels is analyzed for different cases. Optimization method is employed to relax the requirements on the network topology and to determine the minimum of such lower bound for each case, respectively. Simulation examples are also presented to illustrate the established results.

Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control

This paper concerns the problem of exponential synchronization for a class of general delayed dynamical networks with hybrid coupling via pinning periodically intermittent control. Both the internal delay and coupling delay are taken into account in the network model. Meanwhile, the transmission delay and self-feedback delay are involved in the delayed coupling term. By establishing a new differential inequality, several simple and useful exponential synchronization criteria are derived analytically. It is shown that the controlled synchronization state can vary in comparison with the conventional synchronized solution, and the degree of the node and the inner delayed coupling matrix play important roles in the controlled synchronization state. By choosing different inner delayed coupling matrices and the degrees of the node, different controlled synchronization states can be obtained. Furthermore, the detail pinning schemes deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength are provided. The simple procedures illuminating how to design suitable intermittent controllers in real application are also given. Numerical simulations, including an undirected scale-free network and a directed small-world network, are finally presented to demonstrate the effectiveness of the theoretical results.

Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects

This paper investigates the synchronization problem of coupled switched neural networks (SNNs) with mode-dependent impulsive effects and time delays. The main feature of mode-dependent impulsive effects is that impulsive effects can exist not only at the instants coinciding with mode switching but also at the instants when there is no system switching. The impulses considered here include those that suppress synchronization or enhance synchronization. Based on switching analysis techniques and the comparison principle, the exponential synchronization criteria are derived for coupled delayed SNNs with mode-dependent impulsive effects. Finally, simulations are provided to illustrate the effectiveness of the results.