Bifurcation control of small‐world networks with delays VIA PID controller

In this paper, the problem of bifurcation control for a small‐world network model with time delay is studied. We first put forward a Proportional‐Integral‐Derivative (PID) feedback scheme to control the Hopf bifurcation of the network. The time delay is selected as the bifurcation parameter. The conditions of the stability and Hopf bifurcation are given for the controlled network. By using the center manifold theorem and the normal form theory, the direction and stability of bifurcating periodic solutions are confirmed. The feasible region of the parameters of the controller is determined. It is found that the bifurcation dynamics of the small‐world network are optimized by adjusting the parameters of the PID controller. Finally, a numerical example verifies the effectiveness of the designed PID controller, and the relationships between the onset of the Hopf bifurcation and the control parameters are obtained.     

两种典型网络中三种病毒传播模型的传播特性研究

传染性疾病在人类社会的流行,计算机蠕虫病毒在Internet上的频频爆发,都给人类社会造成了巨大的损失。因此,病毒传播研究一直是国际上科学家所关注的焦点。近年来兴起的复杂网络研究为人类认识病毒传播特征、抑制和防御病毒传播提供了一条新的途径。本文研究了两种典型网络中三种病毒传播模型的传播特性。     

一类二阶时延神经网络的分岔分析和控制

讨论了一类二阶时延网络系统的非线性特性,应用线性化稳定性和分岔理论,提出了该系统从稳定到分岔的条件.结论指出利用延迟时间可以进行分岔控制、极限环幅值控制等,并给出了仿真的具体实例.     

Controllability of Boolean control networks with time delays in states

This paper investigates the controllability of Boolean networks with time-invariant delays in states. After a brief introduction on converting the logic dynamics to discrete time delay systems, the controllability via two kinds of controls is studied. One kind of control is generated by Boolean control networks, another kind of control is free Boolean sequences. In both cases, necessary and sufficient conditions of the controllability of Boolean control networks are proved. Finally, examples are given to illustrate the efficiency of the obtained results.     

指挥控制网络级联失效模型研究*

基于指挥控制网络的拓扑特征和级联失效特点,提出了一种带可调节参数的指挥控制网络级联失效模型。该模型提出了一种考虑节点组织地位的初始负载定义方法,以网络级联失效平均规模和级联失效临界值作为网络的抗毁性度量;通过仿真实验分析了网络负载的层次性、节点过载承受能力、跨级指挥和平行指挥等模型参数对指挥控制网络级联失效行为的影响,为现实指挥控制网络的级联失效行为的研究提供了新的思路。     

考虑远程随机感染的复杂网络上疾病传播行为*

将远程随机感染引入到经典的SIRS模型来研究复杂网络上疾病传播行为,考虑到感染节点在以一定概率把疾病感染到其邻接节点的同时,随机选取网络中一个不存在边连接的非邻接节点,并以一定的远程感染概率进行感染。针对小世界网络和无标度网络,分别采用重连概率相关和度相关的远程感染概率,利用平均场的方法求得改进的SIRS模型在这两种网络上的传播阈值以及稳态感染密度。数值仿真结果表明：对于小世界网络,有效传播率在一定范围内,重连概率对稳态感染密度和传播速度有明显的影响,超过这个范围,重连概率对稳态感染密度的影响可以忽略;而     

规则网络中的SIRS病毒局域控制建模与仿真*

提出一个带有局域控制的二维规则网络SIRS模型,理论分析和计算机仿真都表明局域控制能很好地抑制此模型中的病毒传播。研究发现系统状态随时间的演化最终会达到一个稳定状态;病毒的稳态感染比例与传播效率、被控制个体比例和免役个体失去免役能力的概率有关。只有当传播效率大于一个临界值时,病毒才能在网络中持续传播。     

Bifurcation analysis in a discrete-time single-directional network with delays

In this paper, we consider a simple discrete-time single-directional network of four neurons. The characteristics equation of the linearized system at the zero solution is a polynomial equation involving very high-order terms. We first derive some sufficient and necessary conditions ensuring that all the characteristic roots have modulus less than 1. Hence, the zero solution of the model is asymptotically stable. Then, we study the existence of three types of bifurcations, such as fold bifurcations, flip bifurcations, and Neimark–Sacker (NS) bifurcations. Based on the normal form theory and the center manifold theorem, we discuss their bifurcation directions and the stability of bifurcated solutions. In addition, several codimension two bifurcations can be met in the system when curves of codimension one bifurcations intersect or meet tangentially. We proceed through listing smooth normal forms for all the possible codimension 2 bifurcations.     

Synchronization of complex networks with coupling delays via adaptive pinning intermittent control

The problem of exponential synchronization for a class of general complex dynamical networks with nonlinear coupling delays by adaptive pinning periodically intermittent control is considered in this paper. We use the methods of the adaptive control, pinning control and periodically intermittent control. Based on the piecewise Lyapunov stability theory, some less conservative criteria are derived for the global exponential synchronization of the complex dynamical networks with coupling delays. And several corresponding adaptive pinning feedback synchronization controllers are designed. These controllers have strong robustness against the coupling strength and topological structure of the network. Using the delayed nonlinear system as the nodes of the networks, a numerical example of the complex dynamical networks with nonlinear coupling delays is given to demonstrate the effectiveness of the control strategy.     

复杂网络上的A（H1N1）型流感传播模型研究

研究2009年我国A（H1N1）型流感大流行的病毒传播规律以及预防控制策略,发展复杂网络上的传播动力学理论,以提高应对类似甲流的、突发的世界公共卫生危机的能力。建立基于复杂网络的小世界效应和无标度特性的SIRD病毒传播模型,采用中国疾病预防控制中心的甲流传播数据,选择AnyLogic仿真平台对一个中等规模城市的甲流传播进行仿真实验。仿真数据表明：学校停课、限制人口自由流动、扩大疑似病例的处理范围、接种疫苗等是控制疫情大爆发的有效措施,并存在控制强度的临界值。     

SIS model of epidemic spreading on dynamical networks with community

We present a new epidemic Susceptible-Infected-Susceptible (SIS) model to investigate the spreading behavior on networks with dynamical topology and community structure. Individuals in themodel are mobile agentswho are allowed to perform the inter-community (i.e., long-range) motion with the probability p. The mean-field theory is utilized to derive the critical threshold (λ _C ) of epidemic spreading inside separate communities and the influence of the long-range motion on the epidemic spreading. The results indicate that λ _C is only related with the population density within the community, and the long-range motion will make the original disease-free community become the endemic state. Large-scale numerical simulations also demonstrate the theoretical approximations based on our new epidemic model. The current model and analysis will help us to further understand the propagation behavior of real epidemics taking place on social networks.     

Synchronisation of complex dynamical networks with additive stochastic time-varying delays

In this letter, a class of complex dynamical networks with additive stochastic time-varying delays is investigated. Two kinds of delays in complex dynamical networks are taken into consideration, one is called the nodes-induced delay in this paper, and the other is the network-induced delay. Both of the delays are assumed to obey different stochastic distributions. By utilising a novel Lyapunov–Krasovskii functional and stochastic analysis techniques, a sufficient criterion is obtained in the form of linear matrix inequalities to ensure the synchronisation of the complex dynamical networks. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Global synchronization of complex networks with interval time-varying delays and stochastic disturbances

The synchronization problem is considered for a class of stochastic complex networks with interval time-varying delays. Based on the Lyapunov functional method and stochastic analysis theory, delay-dependent sufficient conditions are obtained, which ensure that the identical delayed networks are globally synchronized in the mean square sense. Furthermore, the ‘piecewise delay’ approach is improved to deal with the synchronization problem of systems with stochastic disturbances by introducing two new lemmas. The efficiency and applicability of the proposed methodology are demonstrated by two numerical examples.     

SIS model of epidemic spreading on dynamical networks with community

We present a new epidemic Susceptible-Infected-Susceptible (SIS) model to investigate the spreading behavior on networks with dynamical topology and community structure. Individuals in themodel are mobile agentswho are allowed to perform the inter-community (i.e., long-range) motion with the probability p. The mean-field theory is utilized to derive the critical threshold (λ_C) of epidemic spreading inside separate communities and the influence of the long-range motion on the epidemic spreading. The results indicate that λ_C is only related with the population density within the community, and the long-range motion will make the original disease-free community become the endemic state. Large-scale numerical simulations also demonstrate the theoretical approximations based on our new epidemic model. The current model and analysis will help us to further understand the propagation behavior of real epidemics taking place on social networks.     

Bifurcation in model reference adaptive control systems

We study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism. Exact stability boundaries are computed and different routes to chaotic behavior and global instability are described. Typically, we observed a region of period doubling and Hopf bifurcations similar to those observed in the Ziegler-Nichols approach to PID control design. The analysis applies to higher order and certain nonlinear systems as well.     

一类具有饱和发生率的时滞恶意病毒传播模型的分岔控制策略

考虑非线性的饱和发生率,建立一种刻画信息物理融合系统(cyber-physical systems, CPS)中恶意病毒传播的SIRS(susceptible-infected-recovered-susceptible)模型.为了避免因Hopf分岔的产生致使恶意病毒传播扩散,采用参数调节法和状态反馈法相结合的混合分岔控制策略,研究信息物理融合系统的Hopf分岔控制问题,建立受控系统的稳定性条件和分岔判据,探明控制增益参数对Hopf分岔点和分岔极限环幅值的影响规律,并给出分岔阈值与增益参数间的关系图.数值仿真结果表明,所提出的混合分岔控制策略不仅能够改变Hopf分岔点的位置,而且可以有效调节极限环幅值的大小,使得信息物理融合系统产生预期的动力学行为,有效降低恶意病毒传播的危害.     

Synchronisation for complex dynamical networks with hybrid coupling time-varying delays via pinning adaptive control

This paper is concerned with the problem of synchronisation for complex networks with hybrid coupling time delays. The control strategy consisting of adaptive control and pinning adaptive control is considered. Together with an augment Lyapunov–Krasovskii functional and using the effective mathematical techniques, several conditions are derived to guarantee a class of complex dynamical networks with hybrid coupling time-varying delays to be synchronised. Finally, some representative examples are simulated to demonstrate the effectiveness of the proposed approach.     

Stability analysis and H∞ control for hybrid complex dynamical networks with coupling delays

This paper formulates and studies a model of complex dynamical networks with switching topology and coupling delays. Based on the hybrid control and Lyapunov function, the stability and robust H_∞ control of such networks with impulsive and switching effects, which have not been studied before, are addressed with some criteria derived. Examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

自适应复杂网络中的病毒传播模型

提出了一个基于自适应复杂网络的病毒传播模型。模型中,易感节点为了不被感染,能够有意识地避开与感染节点的连接,此过程一方面使得网络结构发生了变化,另一方面网络结构的变化又反过来对病毒传播过程造成了影响。着重考查了模型中个体的躲避行为对病毒传播效果的影响,结果显示,在个体躲避行为的驱动下,系统的最终染病节点数会发生振荡,并且在一定的参数范围内系统出现了双稳状态。     

Pinning weighted complex networks with heterogeneous delays by a small number of feedback controllers

Weighted complex dynamical networks with heterogeneous delays in both continuous-time and discrete-time domains are controlled by applying local feedback injections to a small fraction of network nodes. Some generic stability criteria ensuring delay-independent stability are derived for such controlled networks in terms of linear matrix inequalities （LMIs）, which guarantee that by placing a small number of feedback controllers on some nodes the whole network can be pinned to some desired homogenous states. In some particular cases, a single controller can achieve the control objective. It is found that stabilization of such pinned networks is completely determined by the dynamics of the individual uncoupled node, the overall coupling strength, the inner-coupling matrix, and the smallest eigenvalue of the coupling and control matrix. Numerical simulations of a weighted network composing of a 3-dimensional nonlinear system are finally given for illustration and verification.