复杂网络级联动力学行为机制研究
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摘要
现代人类社会越来越依赖于网络化基础设施,如电力网、通信网、Internet、计算机网络、金融网和交通网等不同网络。随着网络化程度的提高,网络化基础设施的功能越来越强大,网络系统的整体效率得到了大幅提高。然而,这些网络相互依赖、关联的程度也越来越高,内部的动力学特征也变得更加复杂,这增加了网络系统崩溃的可能性。当网络遭到自然灾害、网络攻击、误操作和随机故障等多种外部或内部威胁时,一个小的异常事件,经过级联反应,往往会传播蔓延至整个网络系统,引起大规模的崩溃事故。从动力学角度来看,这种传导性的动力学过程被称为“级联故障(Cascading Failures)”
网络中频频发生的级联性的灾难和故障,造成系统大规模破坏和业务中断,严重威胁到了基础设施网络的安全运行,给国民经济造成了巨额损失。因此,在网络攻击、重大事故、人为疏忽、随机干扰等多种条件下,由于灾变、级联行为导致的网络安全或可生存性问题已经引起各个国家、政府的高度重视,尤其是以美国、欧洲为代表的发达国家将网络安全研究上升为国家战略。同时,该问题也已经成为当前网络安全研究领域中的一个前沿研究热点。
目前对于这种级联行为引起的网络安全研究,大部分局限于网络拓扑结构的鲁棒性和级联反应的结果,而对级联的发展过程的关注比较缺乏,尤其是对于级联事件从涌现、发展、动荡、蔓延等不同阶段中所呈现的动力学演化规律与特征缺乏认识。
本文突破了以往研究的局限性,围绕“网络级联动力学行为”为核心,从动力学角度出发,从引起级联反应的包括外部诱因、内部诱因在内的多种诱导因素入手,使用统计分析与比较分析相结合的方法,遵循从对构建的网络模型的研究再到对真实网络的实证分析的步骤,深入剖析了网络级联行为的动力学演化过程和规律特征。主要包括：揭示了级联行为的生命周期及级联过程中网络崩溃部件的时间特征；探索了网络组件脆弱性和级联动力学行为之间的内在相关性问题,挖掘出了级联过程中的脆弱节点、脆弱链路；为优化有限资源的调度配置,在针对链路的不同攻击策略下,研究了具有应急恢复机制的级联动力学行为过程。本文的工作可以为在重大灾变情况下网络级联故障的应急处理和灾难控制提供重要理论依据。
本文工作的主要创新点如下：
(1)我们揭示了网络级联事件所经历的生命周期及级联过程中网络崩溃部件的时间规律特征。在蓄意攻击和随机故障等多种策略下,分别研究了攻击节点和攻击链路所引起的级联动力学行为过程,发现无论在蓄意攻击还是在随机故障下,Scale-free网络的级联事件的生命周期比ER随机网和WS小世界网络的级联事件的生命周期长；在蓄意攻击下,WS网络和ER随机网中崩溃的节点数或边数,随时间呈现出低-高-低的变化规律。基于节点的蓄意攻击下Scale-free网络的大部分崩溃的节点发生在级联的初始阶段；而在随机攻击下,当网络部件容错能力较大时,Scale-free、WS和ER随机网中大部分崩溃的部件总是发生在级联初始阶段。这一发现对于应对重大事故下的网络级联故障提供了决策依据。
(2)探索了网络链路的脆弱性与网络级联反应之问的内在相关性的问题,以识别出网络级联反应过程中的脆弱链路。针对网络脆弱链路的识别问题,建立了网络链路上有物质负载的级联动力学模型,并定义了四种描述边的特征的方法,在多种攻击策略引导下研究了网络级联反应过程中崩溃链路的特征。发现当链路的容错能力较小时,无论在蓄意攻击或随机故障下,在三种网络模型Scale-free、WS小世界和ER随机网络中,总是那些连接两个端点的介数乘积较小的边或链路比较脆弱,在崩溃的边中所占比例最多；当容错能力较大时,在随机故障中,反而那些连接的两个端点的介数乘积较大的边或链路比较脆弱。这一发现再次验证了众所周知的“木桶原理”。我们的发现,对于挖掘分析出网络潜在的安全隐患,保护边或链路上有流量负载的网络具有重要意义。
(3)探索了网络节点的脆弱性与网络级联动力学之间的内在相关性问题,以识别出网络级联反应过程中脆弱的节点。针对网络脆弱节点的识别问题,建立了网络负载定义在节点上的级联动力学模型,并定义了四种刻画网络节点特征的方法,从多种针对节点的攻击策略入手,研究了在级联过程中崩溃节点的具有的特征。发现在蓄意攻击下,对于Scale-free网络,本文定义的第四种权重特征较小的节点比较脆弱,对无标度特征的真实网络的仿真分析也进一步验证了我们的结论；对于WS和ER网络,当节点的容错能力较小时,第四种权重特征较小且度数较大的节点比较脆弱。而在随机故障下,这三种网络中,反而那些度数较大的节点比较脆弱。我们的发现对于挖掘分析网络潜在的安全隐患,保护负载定义在节点上的各种网络提供了重要理论依据。
(4)在有限外部资源的条件下,首次提出了应对网络链路遭到攻击引起的网络级联故障灾害的应急策略。由于应对级联故障需要考虑到成本的问题,这需要根据各个个体之间安全能力的差异,来优化资源调度配置。因此,针对幂律分布特征的Scale-free网络,在外部可用资源有限的条件下,首次提出了应对基于边攻击引起的网络级联故障灾害的应急策略方案,根据边的特征优化配置安全资源,以提高网络应对级联的能力。发现,当有限资源按照本文提出的第四种策略分配时,能够有效地维持网络的连通性,有效地控制级联传播的速度,并能有效控制级联传播的过程,控制崩溃的爆发。随后,对无标度特征的真实网络的仿真分析进一步验证了我们的结论。
综上所述,本文所揭示的网络级联行为过程中的动力学规律和特征,为保障如电力网、通讯网、Internet、交通网等关键基础设施网络的安全运行提供了重要理论依据。同时,在日益开放、复杂、动态的网络环境下,为研究各种异常行为导致的网络行为安全问题、研究基于网络化思维的信息安全提供了新的理论与方法。
Modern society increasingly relies on network infrastructures that include the power grids, communication networks, Internet, computer networks, financial networks and traffic networks. As the netware-based degree improves, the function of network infrastructures becomes more and more powerful and the overall efficiency of network systems has been greatly enhanced. However, the interdependence and interconnection among networks is increasing and the internal dynamics of networks has become more complex. As a result, all of these facts increase the possibility of collapse in network systems. When the networks are subjected to many kinds of external or internal disasters and threats, such as the extreme weather, malicious attacks and disruptions, artificial misoperations and random faults, it will lead to serious consequences. Even a small abnormal event, through cascade, will spread through the whole network systems and result in large-scale collapse. From the aspect of dynamics, the process of conductivity is called as "Cascading Failures".
The cascading failures or disasters emerged frequently in networks always destroyed the systems, caused the interruption of service, severely threatened the safe running of infrastructure networks and caused huge economic loss. Therefore, under the conditions of network attacks, serious accidents, human negligence and random breakdown and so on, the network security or survivability resulting from reckoning behavior and cascading failures has attracted great attention of many countries and the governments. Especially, the United States and Europe, as the representatives of the developed countries, have raised the focus on the network survivability anti-destroying ability to national strategy plan. At the same time, it has become the front and hotspot in area of the network security.
At present, the research on network security resulting from cascading behaviors mainly focuses on the robustness of network topological structures and the results of cascading failures. However, there is lack of attention to the evolutional process of cascading dynamics. Especially, for the evolutional rules and characteristics of cascade events showed in different stages from emerging, developing, oscillating and outbreaking, there is lack of understanding.
From the aspect of dynamics, this work breaks through the limitations of previous research, takes "the cascading dynamics and behaviors of complex networks" as the core and focuses on the evolution process of cascading failures. Combining the statistical analysis with comparative analysis and following the steps from studying the network models constructed to studying to the empirical analysis of the steps, this work starts from the main factors of inducing the cascading failures including the internal and external factors, and then investigates the process of the dynamics, the evolution rules and characteristics for network collapse. The main research is listed below. Firstly, we reveal the lifecycle of cascading failures and the time features of broken components of networks in the cascading process. Secondly, we dig out the vulnerable nodes and vulnerable links in cascading process by exploring the inner relationship between the, vulnerability of network components and the broken form of networks. Thirdly, induced by different attacks on the links in networks, we investigate the process of cascading dynamics with emergent recovery mechanism to optimize the schedule and configuration of limited external resources. The work can provide the important theory for emergent response and control of cascading failures under the major disaster.
The main innovation points of this work are as followed:
(1) This work explores the life cycle of the cascading failures and the time features of broken components of networks in the cascading process. We study the process of cascading dynamics induced by attacking the nodes and the links in networks, respectively. As a result, we find that, under both intentional attack and random breakdown, the life cycle of cascade in Scale-free networks is always longer than that both in ER random networks and WS small-world networks. Under the intentional attack, the number of the avalanche edges or nodes in both WS small-world networks and ER random networks always reach a peak over a period of time. Under node-targeted attack, most of the avalanche nodes in Scale-free networks always occur at the beginning of the cascading failures. While under random breakdown, most of the avalanche nodes or links in Scale-free, WS small-world and ER networks always occur at the beginning of the cascading failures as the nodes and links have high tolerance. The results have great significance for protecting key infrastructure networks.
(2) This work probes the inner relationship between the vulnerability of the links and the cascading failures in networks in order to identify the vulnerable links in cascading propagation. For the question that how to identify the vulnerable links in networks, we model the cascading dynamics for the physical load assigned to the edges in networks and define four kinds of weighting methods to characterize the features of the edges. The feature of the avalanche edges in cascading propagation is investigated under various attacking strategies. We find that, as the links have weak tolerance, for Scale-free, WS and ER networks under both intentional attack and random breakdown, the links with small product of betweenness centrality of its two ends will be vulnerable and they have the highest proportion of the avalanche links. On the other hand, as the links have high tolerance, under random breakdown, the links with high product of betweenness centrality of its two ends will be vulnerable. The results verify the known "barrel principle" again. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the links.
(3) This work probes the inner relationship between the vulnerability of the nodes and the cascading failures in networks in order to identify the vulnerable nodes in cascading propagation. For the question that how to identify the vulnerable nodes in networks, we modeled the cascading dynamics for the physical load assigned to the nodes in networks and defined four kinds of weighting methods to characterize the features of the nodes. The feature of the avalanche nodes in cascading propagation is investigated under various attacking strategies on nodes. We find that, for Scale-free networks under intentional attack, the nodes with small value for the fourth kind of weighting method are vulnerable. The numerical simulations of the real network with scale-free characteristics verify the findings; While for WS small-world and ER networks under intentional attack, as the nodes have weak tolerance, the nodes with high degree and small value for the fourth weight are vulnerable. On the other hand, under random breakdown, the nodes with high degree will be vulnerable. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the nodes.
(4) With limited external resources, the emergency strategy of the response of the cascading failures induced by the attacks on the links in networks is presented. In fact, it needs to optimize the resource configuration according to the difference of safety ability among the individuals. Therefore, for the Scale-free networks with power-law degree distribution, under the condition of limited resources, we present the emergency response of the cascading failures induced by edge-based attack, in which, we optimize the resources according to the characteristics of edges in order to improve the ability of dealing with the failures. As a result, as the external resources are deployed to the edges according to the fourth kind of strategy, the external resources can effectively maintain network connectivity, control the velocity of the cascade propagation and control the outbreak of collapse in network. Then, the further numerical simulations of the real networks with scale-free characteristics verify the results.
To sum up, this work reveals the evolution rules and the features of cascading dynamics in the cascade process, which provides the important theory for protecting the safe running of the infrastructure networks such as the power grids, transportation networks, telecommunication networks and Internet. At the same time, in the situation of open, complex and dynamical environment, this work also provides new theory and method for research on both the network behavior security induced by abnormal behaviors and information security based on network thinking.
网络中频频发生的级联性的灾难和故障,造成系统大规模破坏和业务中断,严重威胁到了基础设施网络的安全运行,给国民经济造成了巨额损失。因此,在网络攻击、重大事故、人为疏忽、随机干扰等多种条件下,由于灾变、级联行为导致的网络安全或可生存性问题已经引起各个国家、政府的高度重视,尤其是以美国、欧洲为代表的发达国家将网络安全研究上升为国家战略。同时,该问题也已经成为当前网络安全研究领域中的一个前沿研究热点。
目前对于这种级联行为引起的网络安全研究,大部分局限于网络拓扑结构的鲁棒性和级联反应的结果,而对级联的发展过程的关注比较缺乏,尤其是对于级联事件从涌现、发展、动荡、蔓延等不同阶段中所呈现的动力学演化规律与特征缺乏认识。
本文突破了以往研究的局限性,围绕“网络级联动力学行为”为核心,从动力学角度出发,从引起级联反应的包括外部诱因、内部诱因在内的多种诱导因素入手,使用统计分析与比较分析相结合的方法,遵循从对构建的网络模型的研究再到对真实网络的实证分析的步骤,深入剖析了网络级联行为的动力学演化过程和规律特征。主要包括：揭示了级联行为的生命周期及级联过程中网络崩溃部件的时间特征；探索了网络组件脆弱性和级联动力学行为之间的内在相关性问题,挖掘出了级联过程中的脆弱节点、脆弱链路；为优化有限资源的调度配置,在针对链路的不同攻击策略下,研究了具有应急恢复机制的级联动力学行为过程。本文的工作可以为在重大灾变情况下网络级联故障的应急处理和灾难控制提供重要理论依据。
本文工作的主要创新点如下：
(1)我们揭示了网络级联事件所经历的生命周期及级联过程中网络崩溃部件的时间规律特征。在蓄意攻击和随机故障等多种策略下,分别研究了攻击节点和攻击链路所引起的级联动力学行为过程,发现无论在蓄意攻击还是在随机故障下,Scale-free网络的级联事件的生命周期比ER随机网和WS小世界网络的级联事件的生命周期长；在蓄意攻击下,WS网络和ER随机网中崩溃的节点数或边数,随时间呈现出低-高-低的变化规律。基于节点的蓄意攻击下Scale-free网络的大部分崩溃的节点发生在级联的初始阶段；而在随机攻击下,当网络部件容错能力较大时,Scale-free、WS和ER随机网中大部分崩溃的部件总是发生在级联初始阶段。这一发现对于应对重大事故下的网络级联故障提供了决策依据。
(2)探索了网络链路的脆弱性与网络级联反应之问的内在相关性的问题,以识别出网络级联反应过程中的脆弱链路。针对网络脆弱链路的识别问题,建立了网络链路上有物质负载的级联动力学模型,并定义了四种描述边的特征的方法,在多种攻击策略引导下研究了网络级联反应过程中崩溃链路的特征。发现当链路的容错能力较小时,无论在蓄意攻击或随机故障下,在三种网络模型Scale-free、WS小世界和ER随机网络中,总是那些连接两个端点的介数乘积较小的边或链路比较脆弱,在崩溃的边中所占比例最多；当容错能力较大时,在随机故障中,反而那些连接的两个端点的介数乘积较大的边或链路比较脆弱。这一发现再次验证了众所周知的“木桶原理”。我们的发现,对于挖掘分析出网络潜在的安全隐患,保护边或链路上有流量负载的网络具有重要意义。
(3)探索了网络节点的脆弱性与网络级联动力学之间的内在相关性问题,以识别出网络级联反应过程中脆弱的节点。针对网络脆弱节点的识别问题,建立了网络负载定义在节点上的级联动力学模型,并定义了四种刻画网络节点特征的方法,从多种针对节点的攻击策略入手,研究了在级联过程中崩溃节点的具有的特征。发现在蓄意攻击下,对于Scale-free网络,本文定义的第四种权重特征较小的节点比较脆弱,对无标度特征的真实网络的仿真分析也进一步验证了我们的结论；对于WS和ER网络,当节点的容错能力较小时,第四种权重特征较小且度数较大的节点比较脆弱。而在随机故障下,这三种网络中,反而那些度数较大的节点比较脆弱。我们的发现对于挖掘分析网络潜在的安全隐患,保护负载定义在节点上的各种网络提供了重要理论依据。
(4)在有限外部资源的条件下,首次提出了应对网络链路遭到攻击引起的网络级联故障灾害的应急策略。由于应对级联故障需要考虑到成本的问题,这需要根据各个个体之间安全能力的差异,来优化资源调度配置。因此,针对幂律分布特征的Scale-free网络,在外部可用资源有限的条件下,首次提出了应对基于边攻击引起的网络级联故障灾害的应急策略方案,根据边的特征优化配置安全资源,以提高网络应对级联的能力。发现,当有限资源按照本文提出的第四种策略分配时,能够有效地维持网络的连通性,有效地控制级联传播的速度,并能有效控制级联传播的过程,控制崩溃的爆发。随后,对无标度特征的真实网络的仿真分析进一步验证了我们的结论。
综上所述,本文所揭示的网络级联行为过程中的动力学规律和特征,为保障如电力网、通讯网、Internet、交通网等关键基础设施网络的安全运行提供了重要理论依据。同时,在日益开放、复杂、动态的网络环境下,为研究各种异常行为导致的网络行为安全问题、研究基于网络化思维的信息安全提供了新的理论与方法。
Modern society increasingly relies on network infrastructures that include the power grids, communication networks, Internet, computer networks, financial networks and traffic networks. As the netware-based degree improves, the function of network infrastructures becomes more and more powerful and the overall efficiency of network systems has been greatly enhanced. However, the interdependence and interconnection among networks is increasing and the internal dynamics of networks has become more complex. As a result, all of these facts increase the possibility of collapse in network systems. When the networks are subjected to many kinds of external or internal disasters and threats, such as the extreme weather, malicious attacks and disruptions, artificial misoperations and random faults, it will lead to serious consequences. Even a small abnormal event, through cascade, will spread through the whole network systems and result in large-scale collapse. From the aspect of dynamics, the process of conductivity is called as "Cascading Failures".
The cascading failures or disasters emerged frequently in networks always destroyed the systems, caused the interruption of service, severely threatened the safe running of infrastructure networks and caused huge economic loss. Therefore, under the conditions of network attacks, serious accidents, human negligence and random breakdown and so on, the network security or survivability resulting from reckoning behavior and cascading failures has attracted great attention of many countries and the governments. Especially, the United States and Europe, as the representatives of the developed countries, have raised the focus on the network survivability anti-destroying ability to national strategy plan. At the same time, it has become the front and hotspot in area of the network security.
At present, the research on network security resulting from cascading behaviors mainly focuses on the robustness of network topological structures and the results of cascading failures. However, there is lack of attention to the evolutional process of cascading dynamics. Especially, for the evolutional rules and characteristics of cascade events showed in different stages from emerging, developing, oscillating and outbreaking, there is lack of understanding.
From the aspect of dynamics, this work breaks through the limitations of previous research, takes "the cascading dynamics and behaviors of complex networks" as the core and focuses on the evolution process of cascading failures. Combining the statistical analysis with comparative analysis and following the steps from studying the network models constructed to studying to the empirical analysis of the steps, this work starts from the main factors of inducing the cascading failures including the internal and external factors, and then investigates the process of the dynamics, the evolution rules and characteristics for network collapse. The main research is listed below. Firstly, we reveal the lifecycle of cascading failures and the time features of broken components of networks in the cascading process. Secondly, we dig out the vulnerable nodes and vulnerable links in cascading process by exploring the inner relationship between the, vulnerability of network components and the broken form of networks. Thirdly, induced by different attacks on the links in networks, we investigate the process of cascading dynamics with emergent recovery mechanism to optimize the schedule and configuration of limited external resources. The work can provide the important theory for emergent response and control of cascading failures under the major disaster.
The main innovation points of this work are as followed:
(1) This work explores the life cycle of the cascading failures and the time features of broken components of networks in the cascading process. We study the process of cascading dynamics induced by attacking the nodes and the links in networks, respectively. As a result, we find that, under both intentional attack and random breakdown, the life cycle of cascade in Scale-free networks is always longer than that both in ER random networks and WS small-world networks. Under the intentional attack, the number of the avalanche edges or nodes in both WS small-world networks and ER random networks always reach a peak over a period of time. Under node-targeted attack, most of the avalanche nodes in Scale-free networks always occur at the beginning of the cascading failures. While under random breakdown, most of the avalanche nodes or links in Scale-free, WS small-world and ER networks always occur at the beginning of the cascading failures as the nodes and links have high tolerance. The results have great significance for protecting key infrastructure networks.
(2) This work probes the inner relationship between the vulnerability of the links and the cascading failures in networks in order to identify the vulnerable links in cascading propagation. For the question that how to identify the vulnerable links in networks, we model the cascading dynamics for the physical load assigned to the edges in networks and define four kinds of weighting methods to characterize the features of the edges. The feature of the avalanche edges in cascading propagation is investigated under various attacking strategies. We find that, as the links have weak tolerance, for Scale-free, WS and ER networks under both intentional attack and random breakdown, the links with small product of betweenness centrality of its two ends will be vulnerable and they have the highest proportion of the avalanche links. On the other hand, as the links have high tolerance, under random breakdown, the links with high product of betweenness centrality of its two ends will be vulnerable. The results verify the known "barrel principle" again. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the links.
(3) This work probes the inner relationship between the vulnerability of the nodes and the cascading failures in networks in order to identify the vulnerable nodes in cascading propagation. For the question that how to identify the vulnerable nodes in networks, we modeled the cascading dynamics for the physical load assigned to the nodes in networks and defined four kinds of weighting methods to characterize the features of the nodes. The feature of the avalanche nodes in cascading propagation is investigated under various attacking strategies on nodes. We find that, for Scale-free networks under intentional attack, the nodes with small value for the fourth kind of weighting method are vulnerable. The numerical simulations of the real network with scale-free characteristics verify the findings; While for WS small-world and ER networks under intentional attack, as the nodes have weak tolerance, the nodes with high degree and small value for the fourth weight are vulnerable. On the other hand, under random breakdown, the nodes with high degree will be vulnerable. The results will be important for analyzing the potential safety problems and protecting the networks with the load assigned to the nodes.
(4) With limited external resources, the emergency strategy of the response of the cascading failures induced by the attacks on the links in networks is presented. In fact, it needs to optimize the resource configuration according to the difference of safety ability among the individuals. Therefore, for the Scale-free networks with power-law degree distribution, under the condition of limited resources, we present the emergency response of the cascading failures induced by edge-based attack, in which, we optimize the resources according to the characteristics of edges in order to improve the ability of dealing with the failures. As a result, as the external resources are deployed to the edges according to the fourth kind of strategy, the external resources can effectively maintain network connectivity, control the velocity of the cascade propagation and control the outbreak of collapse in network. Then, the further numerical simulations of the real networks with scale-free characteristics verify the results.
To sum up, this work reveals the evolution rules and the features of cascading dynamics in the cascade process, which provides the important theory for protecting the safe running of the infrastructure networks such as the power grids, transportation networks, telecommunication networks and Internet. At the same time, in the situation of open, complex and dynamical environment, this work also provides new theory and method for research on both the network behavior security induced by abnormal behaviors and information security based on network thinking.
引文
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