Finite-time synchronization control of complex dynamical networks with time delay

In this paper, the finite-time synchronization between two complex networks with non-delayed and delayed coupling is proposed by using the impulsive control and the periodically intermittent control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. Especially, the traditional synchronization criteria are improved by using the impulsive control and the periodically intermittent control in the convergence time, the results of this paper are important. Finally, numerical examples are given to verify the effectiveness and correctness of the synchronization criteria.     

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.     

Synchronization control for the competitive complex networks with time delay and stochastic effects

The synchronization control problem for the competitive complex network with time delay and stochastic effects is investigated by using the stochastic technique and Lyapunov stability theory. The competitive complex network means that the dynamical varying rate of a part of nodes is faster than other nodes. Some synchronization criteria are derived by the full controller and pinning controller, respectively, and these criteria are convenient to be used for concision. A numerical example is provided to illustrate the effectiveness of the method proposed in this paper.     

Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation

In this paper, the generalized outer synchronization between two different delay-coupled complex dynamical networks with noise perturbation is investigated. With a nonlinear control scheme, the sufficient condition for almost sure generalized outer synchronization is developed based on the LaSalle-type invariance principle for stochastic differential equations. Numerical examples are examined to illustrate the effectiveness of the analytical results. The theoretic result is also applied to investigate the outer synchronization between two delay-coupled Hindmarsh–Rose neuronal networks with noise perturbation.     

Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

This paper investigates the problem of function projective synchronization for general complex dynamical networks with time delay. A hybrid feedback control method is designed to achieve function projective synchronization for complex dynamical networks, one with constant time delay and one with time-varying coupling delay. Numerical examples are provided to show the effectiveness of the proposed method.     

Epidemic spreading of an SEIRS model in scale-free networks

An SEIRS epidemic model on the scale-free networks is presented, where the active contact number of each vertex is assumed to be either constant or proportional to its degree for this model. Using the analytical method, we obtain the two threshold values for above two cases and find that the threshold value for constant contact is independent of the topology of the underlying networks. The existence of positive equilibrium is determined by threshold value. For a finite size of scale-free network, we prove the local stability of disease-free equilibrium and the permanence of the disease on the network. Furthermore, we investigate two major immunization strategies, random immunization and targeted immunization, some similar results are obtained. The simulation shows the positive equilibrium is stable.     

Performance analysis of multi-frame message spreading in delay tolerant networks

Communication opportunities in delay tolerant networks are uncertain, so the message is transmitted in a store-carry-forward way, which depends on the contact between nodes. To use the contact efficiently, the message is often divided into many bundles, which are very small and can be transmitted successfully in one contact. Such multi-frame spreading algorithm is very important, but state of the art works just assume that the message is very small and has only one bundle. This paper proposes a theoretical framework based on mean field limit to evaluate the epidemic-like multi-frame spreading algorithm for the first time. In addition, the selfish behaviors can have certain impact on the store-carry-forward communication mode, so we extend our model to the case that nodes are selfish. Simulations show the accuracy of our model. Numerical results show that the more bundles the message has, the lower the average delivery ratio will be. In addition, the selfish behaviors can make the performance be worse.     

Stability analyses of cellular neural networks with continuous time delay

The stability of cellular neural networks (CNNs) with continuous time delay is investigated in the present paper. A main theorem together with a few corollaries related to the existence and boundedness of the solution for this kind of CNNs, as well as its global asymptotic stability is derived. Some numerical simulation examples aimed at justifying the theoretical results are also given.     

Some remarks on global asymptotic stability of neural networks with constant time delay

An elegant proof of a previously reported criterion for the uniqueness and global asymptotic stability of the equilibrium point of a class of neural networks with constant time delay is presented. The present proof yields some interesting observations.     

Exponential stability and periodicity of cellular neural networks with time delay

This paper investigates the problem of exponential stability and periodicity for a class of delayed cellular neural networks (DCNN’s). By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via constructing Lyapunov functional. Those conditions suitable are associated with some initial value and are represented by some blocks of the interconnection matrix. Two examples are discussed to illustrate the main results.     

混沌时滞随机神经网络同步控制

研究了一类混沌时滞随机神经网络同步控制问题．采用更具一般性的时滞反馈控制器,通过巧妙地构造Lyapunov数,分别得到了均方指数同步和均方渐近同步两个判别准则．仿真例子表明,新准则是有效的．     

Local and global synchronization in general complex dynamical networks with delay coupling

Local and global synchronization of complex dynamical networks are studied in this paper. Some simple yet generic criteria ensuring delay-independent and delay-dependent synchronization are derived in terms of linear matrix inequalities (LMIs), which can be verified easily via interior-point algorithm. The assumption that the coupling configuration matrix is symmetric and irreducible, which is frequently used in other literatures, is removed. A network with a fixed delay and a special coupling scheme is given as an example to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.     

Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes

This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.     

Epidemic outbreaks on networks with effective contacts

In real-world networks of disease transmission, the incidence of infection among individuals conforms to a certain fixed probability of effective contact between them, which must meet some necessary conditions for the disease to continue to spread. Based on susceptible/infective/removed (SIR) models in homogeneous or heterogeneous networks, we find that these models evolve dynamically just like in networks without connectivity fluctuations if all the susceptible individuals are supposed to have the same effective contact. This means that effectively heterogeneous contacts play a striking role in epidemic dynamics. To go a step further, we introduce the effective contact function (ECF) into models and present an analytical and numerical study for the threshold and dynamical behaviors of epidemic incidence. The power-law and proportional ECFs are considered, and, we demonstrate analytically that the epidemic incidence is generally a monotone decreasing function of the epidemic threshold and increasing function of the number of effective contacts. Certain exceptional cases are also discussed. This tells us that we cannot always focus on the threshold to evaluate the extent of epidemic outbreaks.     

Robust exponential stability analysis of discrete-time switched Hopfield neural networks with time delay

The robust exponential stability problem in this paper for discrete-time switched Hopfield neural networks with time delay and uncertainty is considered. Firstly, the mathematical model of the system is established. Then by constructing a new Lyapunov–Krasovskii functional, some new delay-dependent criteria are developed, which guarantee the robust exponential stability of discrete-time switched Hopfield neural networks. A numerical example is provided to demonstrate the potential and effectiveness of the results obtained.     

Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

In this paper, we study the spreading of infections in complex heterogeneous networks based on an SIRS epidemic model with birth and death rates. We find that the dynamics of the network-based SIRS model is completely determined by a threshold value. If the value is less than or equal to one, then the disease-free equilibrium is globally attractive and the disease dies out. Otherwise, the disease-free equilibrium becomes unstable and in the meantime there exists uniquely an endemic equilibrium which is globally asymptotically stable. A series of numerical experiments are given to illustrate the theoretical results. We also consider the SIRS model in the clustered scale-free networks to examine the effect of network community structure on the epidemic dynamics.     

An individual-based modeling framework for infectious disease spreading in clustered complex networks

We introduce an individual-based model with dynamical equations for susceptible-infected-susceptible (SIS) epidemics on clustered networks. Linking the mean-field and quenched mean-field models, a general method for deriving a cluster approximation for three-node loops in complex networks is proposed. The underlying epidemic threshold condition is derived by using the quasi-static approximation. Our method thus extends the pair quenched mean-field (pQMF) approach for SIS disease spreading in unclustered networks to the scenario of epidemic outbreaks in clustered systems with abundant transitive relationships.We found that clustering can significantly alter the epidemic threshold, depending nontrivially on topological details of the underlying population structure. The validity of our method is verified through the existence of bounded solutions to the clustered pQMF model equations, and is further attested via stochastic simulations on homogeneous small-world artificial networks and growing scale-free synthetic networks with tunable clustering, as well as on real-world complex networked systems. Our method has vital implications for the future policy development and implementation of intervention measures in highly clustered networks, especially in the early stages of an epidemic in which clustering can decisively alter the growth of a contagious outbreak.