基于超图的超网络相继故障分析

分析了快递超网络和电子元件超网络的相继故障扩散方式, 结合超图理论提出了2-section 图分析法和线图分析法, 并仿真分析了无标度超网络耦合映像格子的相继故障进程. 结果表明: 无标度超网络对外部攻击表现出了既鲁棒又脆弱的特性. 针对相继故障的不同扩散方式, 无标度超网络的相继故障行为表现出不同的特点. 超网络的相继故障行为和超网络的超度以及超边度分布有密切的联系, 也和超网络中超边的个数有关. 通过和同规模的Barabasi-Albert (BA)无标度网络对比, 在同一种攻击方式下同规模的无标度超网络都比BA 无标度网络表现出了更强的鲁棒性. 另外, 基于超边扩散的相继故障进程比基于节点扩散的相继故障进程更加缓慢.     

带有层级结构的复杂网络级联失效模型

针对现实世界的网络中普遍存在的层级结构建立一个级联失效模型, 该模型可用于优化金融、物流网络设计. 选择的层级网络模型具有树形骨架和异质的隐含连接, 并且骨架中每层节点拥有的分枝数服从正态分布. 级联失效模型中对底层节点的打击在不完全信息条件下进行, 也即假设打击者无法观察到隐含连接. 失效节点的负载重分配考虑了层级异质性, 它可以选择倾向于向同级或高层级完好节点分配额外负载. 仿真实验表明, 层级网络的拓扑结构随连接参数变化逐渐从小世界网络过渡到随机网络. 网络级联失效规模随隐含连接比例呈现出先增加后降低的规律. 负载重分配越倾向于高层级节点, 网络的抗毁损性越高. 同时, 由于连接参数会改变隐含连接在不同层级之间的分布, 进而对网络的抗毁损性产生显著影响, 为了提高网络抗毁损能力, 设计网络、制定管理控制策略时应合理设定连接参数. 关键词： 复杂网络 级联失效 层级结构     

基于电力网络的级联故障模型

以电力系统的停电事故为例,提出一种节点具有能量耗散和扩容行为的级联故障模型,并分别在二维规则网络和无标度网络上对该系统的演化过程进行计算机模拟.结果表明,在两种不同结构的网络中系统的演化过程都出现了自组织临界现象,说明网络中节点能量的耗散及容量的扩充是导致电力系统出现自组织临界现象的重要因素.此外,还发现无标度网络中的最大级联故障规模要远大于二维规则网络中的级联故障规模.     

Impact of core-periphery structure on cascading failures in interdependent scale-free networks

Core-periphery structure is a typical meso-scale structure in networks. Previous studies on core-periphery structure mainly focus on the improvement of detection methods, while the research on the impact of core-periphery structure on cascading failures in interdependent networks is still missing. Therefore, we investigate the cascading failures of interdependent scale-free networks with different core-periphery structures and coupling preferences in the paper. First, we introduce an evaluation index to calculate the goodness of core-periphery structure. Second, we propose a new scale-free network evolution model, which can generate tunable core-periphery structures, and its degree distribution is analyzed mathematically. Finally, based on a degree-load-based cascading failure model, we mainly investigate the impact of goodness of core-periphery structure on cascading failures in both symmetrical and asymmetrical interdependent networks. Through numerical simulations, we find that with the same average degree, the networks with weak core-periphery structure will be more robust, while the initial load on node will influence the improvement of robustness. In addition, we also find that the inter-similarity coupling performs better than random coupling. These findings may be helpful for building resilient interdependent networks.     

Dynamics of load entropy during cascading failure propagation in scale-free networks

In this Letter, we introduce the concept of load entropy, which can be an average measure of a network's heterogeneity in the load distribution. Then we investigate the dynamics of load entropy during failure propagation using a new cascading failures load model, which can represent the node removal mechanism in many real-life complex systems. Simulation results show that in the early stage of failure propagation the load entropy for a larger cascading failure increases more sharply than that for a smaller one, and consequently the cascading failure with a larger damage can be identified at the early stage of failure propagation according to the load entropy. Particularly, load entropy can be used as an index to be optimized in cascading failures control and defense in many real-life complex networks.     

Cascading failures on weighted urban traffic equilibrium networks

In this paper, we study the cascading failure on weighted urban traffic equilibrium networks by introducing a more practical flow assignment mechanism. The whole process including edges overloading to node malfunctioning, dynamic spanning clustering and the phase transitions trigged with O-D flow evolving is simulated. It is found that there are three districts: slow, fast and stationary (collapse for scale-free networks) cascading failure districts. And different topologies have large effects on the ranges of these districts. Simulations also show that, although the latter can support larger traffic flow, homogeneous networks appear to be more robust against cascading failures than heterogeneous ones.     

基于相继故障信息的网络节点重要度演化机理分析

分析了过载机制下节点重要度的演化机理.首先,在可调负载重分配级联失效模型基础上,根据节点失效后其分配范围内节点的负载振荡程度,提出了考虑级联失效局域信息的复杂网络节点重要度指标.该指标具有两个特点:一是值的大小可以清晰地指出节点的失效后果;二是可以依据网络负载分配范围、负载分配均匀性、节点容量系数及网络结构特征分析节点重要度的演化情况.然后,给出该指标的仿真算法,并推导了最近邻择优分配和全局择优分配规则下随机网络和无标度网络节点重要度的解析表达式.最后,实验验证了该指标的有效性和可行性,并深入分析了网络中节点重要度的演化机理,即非关键节点如何演化成影响网络级联失效行为的关键节点.     

Robustness of Cyber-Physical Supply Networks in Cascading Failures

A cyber-physical supply network is composed of an undirected cyber supply network and a directed physical supply network. Such interdependence among firms increases efficiency but creates more vulnerabilities. The adverse effects of any failure can be amplified and propagated throughout the network. This paper aimed at investigating the robustness of the cyber-physical supply network against cascading failures. Considering that the cascading failure is triggered by overloading in the cyber supply network and is provoked by underload in the physical supply network, a realistic cascading model for cyber-physical supply networks is proposed. We conducted a numerical simulation under cyber node and physical node failure with varying parameters. The simulation results demonstrated that there are critical thresholds for both firm’s capacities, which can determine whether capacity expansion is helpful; there is also a cascade window for network load distribution, which can determine the cascading failures occurrence and scale. Our work may be beneficial for developing cascade control and defense strategies in cyber-physical supply networks.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.     

复杂网络中带有应急恢复机理的级联动力学分析

提出带有应急恢复机理的网络级联故障模型,研究模型在最近邻耦合网络,Erdos-Renyi随机网络,Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为.给出了应急恢复机理和网络效率的定义,并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响.结果表明,模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度,并且提高了网络的恢复能力.而且网络中节点负载容量越大,网络效率降低速度和节点故障率的增长速度越慢.同时,随着节点过载故障概率的减小,网络效率的降低速度和节点故障率的增长速度也逐渐减缓.此外,对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析,结果发现网络拓扑节点度分布的异质化程度的增大,提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度.以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为,为实际网络中级联故障现象的控制和防范提供了参考.     

Tolerance of edge cascades with coupled map lattices methods

This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.     

Attack vulnerability of scale-free networks due to cascading failures

In this paper, adopting the initial load of a node i to be with k_i being the degree of the node i, we propose a cascading model based on a load local redistribution rule and examine cascading failures on the typical network, i.e., the BA network with the scale-free property. We find that the BA scale-free network reaches the strongest robustness level in the case of α=1 and the robustness of the network has a positive correlation with the average degree 〈k〉, where the robustness is quantified by a transition from normal state to collapse. In addition, we further discuss the effects of two different attacks for the robustness against cascading failures on our cascading model and find an interesting result, i.e., the effects of two different attacks, strongly depending to the value α. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.     

基于可调负载重分配的无标度网络连锁效应分析

为了深入研究复杂网络抵制连锁故障的全局鲁棒性,针对现实网络上的负载重分配规则常常是介于全局分配与最近邻分配、均匀分配与非均匀分配的特点,围绕负荷这一影响连锁故障发生和传播最重要的物理量以及节点崩溃后的动力学过程,提出了一种可调负载重分配范围与负载重分配异质性的复杂网络连锁故障模型,并分析了该模型在无标度网络上的连锁故障条件.数值模拟获得了复杂网络抵制连锁故障的鲁棒性与模型中参数的关系.此外,基于网络负载分配规则的分析以及理论解析的推导,验证了数值模拟结论,也证明在最近邻与全局分配两种规则下都存在负载分配均匀性参数等于初始负荷强度参数即β=τ使得网络抵御连锁故障的能力最强.     

Synergetic behavior in the cascading failure propagation of scale-free coupled map lattices

In this paper, the whole dynamical process of cascading failures in a class of scale-free coupled map lattices (CML’s), from the occurrence of attack to the end of failure propagation, is investigated. A dynamical model of cascading failures, based on synergetic theory, is constructed. Numerical simulations show that the macroscopic properties of the scale-free CML’s during cascading failure propagation are governed by the general laws of synergetics. This result will be useful in furthering the studies of the prediction and prevention of cascading events in many real-life complex networks.     

Trajectory Control of Scale-Free Dynamical Networks with Exogenous Disturbances

In this paper, the trajectory control of multi-agent dynamical systems with exogenous disturbances is studied. Suppose multiple agents composing of a scale-free network topology, the performance of rejecting disturbances for the low degree node and high degree node is analyzed. Firstly, the consensus of multi-agent systems without disturbances is studied by designing a pinning control strategy on a part of agents, where this pinning control can bring multiple agents' states to an expected consensus track. Then, theinfluence of the disturbances is considered by developing disturbance observers, and disturbance observers based control (DOBC) are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for scale-free network topology. Finally, by analyzing examples of multi-agent systems with scale-free network topology and exogenous disturbances, the verities of the results are proved. Under the DOBC with the designed parameters, the trajectory convergence of multi-agent systems is researched by pinning two class of the nodes. We have found that it has more stronger robustness to exogenous disturbances for the high degree node pinned than that of the lowdegree node pinned.     

A robust matching model of capacity to defense cascading failure on complex networks

How to control the cascading failure has become a hot topic in recent years. In this paper, we propose a new matching model of capacity by developing a profit function to defense cascading failures on artificially created scale-free networks and the real network structure of the North American power grid. Results show that our matching model can enhance the network robustness efficiently, which is particularly important for the design of networks to deduce the damage triggered by the cascading failures.     

基于综合故障的无线传感器网络无标度容错拓扑模型研究

针对无线传感器网络实际应用中遇到的环境损毁和能量耗尽的问题,本文首先对网络综合故障进行建模,获取满足综合故障容忍能力和网络生命期双重需求的网络节点度和节点度上限值的取值规律,并结合由无标度特征导出的两者关系,从而求得最优节点度上限值,最终引入关于节点度上限值的适应度函数,提出了容忍环境损毁和能量耗尽综合故障的无标度容错拓扑演化模型.仿真实验结果表明,该模型演化生成的无标度拓扑对环境损毁和能量耗尽具有较好的容错性,并能够有效地延长网络生命期.     

Exploring the robustness of urban bus network: A case from Southern China

The robustness of urban bus network is essential to a city that heavily relies on buses as its main transportation solution. In this paper, the urban bus network has been modeled as a directed and space L network, and Changsha, a transportation hub of nearly 8 million people and hundreds of bus lines in southern China, is taken as a case. Based on the quantitative analyses of the topological properties, it is found that Changsha urban bus network is a scale-free network, not a small-world network. To evaluate the robustness of the network, five scenarios of network failure are simulated, including a random failure and four types of intentional attacks that differed in key node identification methods (i.e., unweighted degree or betweenness centrality) and attack strategies (i.e., normal or cascading attack). It is revealed that intentional attacks are more destructive than a random failure, and cascading attacks are more disruptive than normal attacks in the urban bus network. In addition, the key nodes identification methods are found to play a critical role in the robustness of the urban bus network. Specifically, cascading attack could be more disruptive when the betweenness centrality is used to identify key nodes; in contrast, normal attack could be more disruptive when the unweighted degree is used to identify key nodes. Our results could provide reference for risk management of urban bus network.     

Load-redistribution strategy based on time-varying load against cascading failure of complex network

Cascading failure can cause great damage to complex networks, so it is of great significance to improve the network robustness against cascading failure. Many previous existing works on load-redistribution strategies require global information, which is not suitable for large scale networks, and some strategies based on local information assume that the load of a node is always its initial load before the network is attacked, and the load of the failure node is redistributed to its neighbors according to their initial load or initial residual capacity. This paper proposes a new load-redistribution strategy based on local information considering an ever-changing load. It redistributes the loads of the failure node to its nearest neighbors according to their current residual capacity, which makes full use of the residual capacity of the network. Experiments are conducted on two typical networks and two real networks, and the experimental results show that the new load-redistribution strategy can reduce the size of cascading failure efficiently.     

Load-dependent random walks on complex networks

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.