Event‐triggered sampled‐data synchronization of complex networks with uncertain inner coupling and time‐varying delays

Synchronization in complex networks is influenced by higher-order interactions and non-Gaussian perturbations, yet their mechanisms remain unclear. We investigate the synchronization and spike dynamics in a higher-order Kuramoto model subjected to Lévy noise. Using the mean order parameter, mean first-passage time, and basin stability, we identify boundaries distinguishing synchronization and incoherence. The stability index governs the tail heaviness of the probability density function for Lévy noise, while the scale parameter affects the magnitude. Synchronization weakens as the stability index decreases, and even completely disappears when the scale parameter exceeds a critical threshold. By varying coupling, we find bifurcations and hysteresis. Lévy noise smooths the synchronization transitions and requires stronger coupling compared to Gaussian white noise. We then define spikes as extreme excursions of the order parameter and study their statistical and spectral properties. The maximum number of spikes is observed at small-scale parameters. A generalized spectral analysis based on an edit distance algorithm measures the similarity between spike sequences and identifies spike patterns. These findings deepen the understanding of synchronization and extreme events in complex networks driven by non-Gaussian noise. Synchronization in complex networks, crucial for understanding phenomena in systems like neuronal networks and power grids, is affected by higher-order interactions and non-Gaussian perturbations. The authors explore a higher-order Kuramoto model with Lévy noise, revealing how stability and scale parameters influence synchronization, offering insights into network dynamics and extreme events.

In this paper, it is mainly concerned with the issue of mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. The uncertain terms are the unknown topological structure which exists inside the complex network and the external noise is imposed to the network. In order to achieve the mean square modified function projective synchronization of complex dynamical network, a strict feedback controller and novel adaptive control laws are designed based on Lyapunov stability theory, inequality techniques, and the properties of the Weiner process to obtain several novel synchronization criterion. Furthermore, the effectiveness of the proposed control scheme is validated by numerical simulations.

Complex networks have been judiciously developed during the last decades. Much attention has been given to investigate the synchronization of complex networks in recent years. In this paper, by constructing a drive network and a suitable impulsively controlled slave network, several synchronization criteria for the uncertain complex networks have been obtained based on the adaptive-impulsive method. The tracking parameters are realized simultaneously as the synchronization occurs. Particularly, our hypotheses and the proposed adaptive-impulsive control laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.

Fixed-time synchronization of discontinuous complex networks with time-varying delay and disturbances via aperiodically semi-intermittent control is investigated in this paper. Firstly, a novel lemma is introduced to prove the fixed-time stability. Then, based on the new lemma, we design a controller with less terms than that in existing literature in work time (control time) and rest time, deriving some sufficient conditions to realize synchronization of a discontinuous complex network with disturbances within a settling time. Finally, a numerical example is provided to illustrate the correctness and effectiveness of our main result.

The synchronization in complex network model with time-delay nodes is investigated. The model is applicable for two sorts of complex networks. With linear feedback controller and adaptive feedback controller, positive definite functions are designed respectively. The sufficient conditions of synchronization are given by Lyapunov stability theory. Finally, numerical simulations show the effectiveness of the synchronization in complex networks.

Synchronization in complex networks has been investigated for decades. Due to the particularity of the interlinks between networks, the synchronization in interdependent networks has received increasing interest. Since the interlinks are not always symmetric in interdependent networks, we focus on the synchronization in unidirectional interdependent networks to study the control scheme. The mathematical model is put forward and some factors are taken into consideration, such as different coupling functions and strengths. Firstly, the feasibility of the control scheme is proved theoretically by using Lyapunov stability theory and verified by simulations. Then, we find that the synchronization could be maintained in one sub-network by utilizing our control scheme while the nodes in the other sub-network are in chaos. The result indicates that the influence of interlinks can be decreased and the proposed scheme can guarantee the synchronization in one sub-network at least. Moreover, we also discuss the robust of our control scheme against the cascading failure. The scheme is verified by simulations to be effective while the disturbances occur.

This document contains corrections to the paper entitled “Contraction Theory and the Master Stability Function: Linking Two Approaches to Study Synchronization in Complex Networks.” The results reported here should substitute those included in Section V-B therein.

A discrete-time neural sliding-mode pinning controller for synchronization of uncertain complex networks with nonidentical nodes is proposed. To achieve synchronization, a neural control scheme constituted by a Recurrent High-Order Neural Network identifier trained with an extended Kalman algorithm, and a discrete-time sliding-mode controller is used in a small fraction of nodes. The applicability of the proposed scheme is illustrated via simulations, using a network constituted by 8-nodes with four different types of chaotic systems.

This paper concentrates on the cluster synchronization such that each community achieves linear-generalized synchronization in complex networks. Here two control schemes are introduced to realize cluster synchronization. One is to adjust the coupling strength of edges which connect different groups automatically, and to use the pinning control simultaneously. The other scheme is to adjust the coupling strength of edges in each group and to select only one node in each group to control. Finally, we present some simulations to demonstrate the correction of our conclusion.

This paper investigates the stabilization and synchronization of positive complex networks with dynamic links. A class of positive complex networks is constructed by introducing dynamic link between nodes. A controller and the corresponding coupling term with respect to links are designed to achieve the positivity and stability of complex networks and link systems, respectively. Then, a synchronization controller and the corresponding coupling term with respect to links and node states are proposed, respectively. The main contributions are as follows: (i) A novel coupling term is constructed to achieve stability and synchronization of positive complex networks, (ii) A stabilization and synchronization framework is constructed by designing two classes of controllers and coupling terms, and (iii) A tractable design, analysis, and computation method is introduced by virtue of linear programming and copositive Lyapunov function. Finally, a simulation example is provided to verify the effectiveness and feasibility of the proposed approaches.

This note investigates finite-time synchronization (FTS) between two uncertain complex networks based on a special unilateral coupling control method. The two networks contain nonidentical nodes, time-varying coupling delayed, unknown parameters and uncertain topological structure. According to the finite-time stability theory and LaSalle’s principle, an effective unilateral coupling control scheme and corresponding adaptive laws are proposed to guarantee the FTS. Simultaneously, the unknown parameters are estimated successfully and the weight values of uncertain topology can automatically adaptive to the suitable value. Finally, simulation results are shown the correctness of the theoretical method.

In this paper, pinning synchronization of complex networks is investigated from a moment‐based analysis approach. The analytical expressions for the first three expected moments of the coupling and control matrix for an ER random graph, a Chung‐Lu random network, and an NW small‐world network are derived, respectively. The shape of the eigenvalue distribution of the coupling and control matrix can be estimated based on the obtained expected moments and thus used to predict pinning synchronization in the network. It is shown that the expected moments are associated with the local structural properties of the network and the control mechanism. This allows us to bound the smallest and largest eigenvalues of the spectral distribution without computing the Laplacian eigenvalues of a large‐scale network. Numerical simulations of the above three representative networks composing of chaotic systems, respectively, are shown for illustration and verification.

This article is concerned with the problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks by improving FXT stability and developing simple control schemes. First, some more relaxed conditions for FXT stability are established and several more accurate estimates for the settling time (ST) are obtained by means of some special functions. Based on the improved FXT stability, FXT synchronization for discontinuous networks is discussed by designing a simple controller without a linear feedback term. Besides, the PAT synchronization is also explored by developing several nontrivial control protocols with finite control gains, where the synchronized time can be prespecified according to actual needs and is irrelevant with any initial value and any parameter. Finally, the improved FXT stability and the synchronization for complex networks are confirmed by two numerical examples.

<p style='text-indent:20px;'>In this paper, a unified theoretical method is presented to implement the finite/fixed-time synchronization control for complex networks with uncertain inner coupling. The quantized controller and the quantized adaptive controller are designed to reduce the control cost and save the channel resources, respectively. By means of the linear matrix inequalities technique, two sufficient conditions are proposed to guarantee that the synchronization error system of the complex networks is finite/fixed-time stable in virtue of the Lyapunov stability theory. Moreover, two types of setting time, which are dependent and independent on the initial values, are given respectively. Finally, the effectiveness of the control strategy is verified by a simulation example.</p>

This article investigates the synchronization of semi-Markovian switching complex networks with partial unknown transition rates. Different from Markovian switching system, semi-Markov process is characterized by a fixed transition probability matrix and a probability density function of the sojoturn time, and the sojourn time obeys an expanded exponential distribution, which relaxes the restriction that the sojoturn time obeys memoryless exponential distribution. To realize synchronization, event-triggered control is applied which effectively reduced the control cost. It is demonstrated that the semi-Markovian switching complex networks can realize synchronization under appropriate control gain, event-triggered parameter and average sojourn time. Besides, to cope with the uncertainties that may occur during the switching process, the synchronization of the semi-Markovian switching complex networks with parameter uncertainties and external disturbances is also discussed. In the end, two simulation examples are provided to verify the feasibility of our results.