移动电话病毒的传播模型研究

对利用蓝牙进行传播的移动电话病毒传播模型进行了研究。针对移动这一重要特性,首先分析了现有模型的不足之处,通过修正Kephart和White的模型（KW模型）以及率方程模型中参数的含义得到了两个修正的模型：随机图和无标度（SF）网上移动病毒传播模型。理论和模拟的结果表明,因为移动性使带病节点和易感节点充分混和,使得模拟结果和理论模型更加接近,证实了移动环境移动速度对病毒传播的效果。     

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。     

通用有效的动态系统网络病毒传播模型方法研究*

研究了依存于网络拓扑的病毒传播特征,并提出了一个通用的动态系统网络模型。该模型对爆发一种病毒后,其是很快灭亡还是长期生存,给出了一个简单易求的传播临界值来进行判断。最后通过对多个网络实际数据集进行计算机仿真,证明了本模型及传播临界值的有效性和精确性。     

复杂动态网络演化社团结构探测分析的研究进展

针对复杂动态网络中演化社团结构的探测,综述了该新领域的研究进展。首先对演化社团结构探测进行了问题描述,总结了四种研究思路。重点介绍了其中一些有代表性的分析方法及其特点,以及衡量探测方法好坏的基准图。最后指出该领域值得进一步探索的研究方向。     

复杂网络上具有多感染阶段的传染病传播模型

针对传染病传播模型缺乏多感染阶段的不足,结合SIR和SEIR两种传播模型的特性,提出了一种改进的具有多感染阶段的SIR传染病传播模型(即SInR模型)。该模型充分考虑了不同感染阶段的非均匀感染力对不同网络结构上传染病传播及传播阈值的影响;同时引入相对感染力及传播时间尺度的概念,从网络结构、网络规模及相对感染力方面进行了仿真研究。仿真中无标度网络采用BA模型的生成算法,而小世界网络采用WS模型的生成算法。由仿真可知,感染节点在整个感染过程中大致服从泊松分布,因此在SInR模型下无标度网络的传播速度更快,范围更广;相对感染力对于传染病的大规模爆发存在着一个阈值,当感染力大于阈值时传染病才能大范围地爆发传播,而小于阈值时传染病只会局域小范围传播直至消失,无标度网络的感染力阈值为0.2,小世界网络的感染力阈值为0.24;随着网络规模的增大,传播时间尺度也在增大,相应的传播速度就会降低。仿真结果表明:该模型下无标度网络传染病传播速度更快且影响范围更大;无标度网络的相对传染力的传播阈值小于小世界网络,设置合理阈值有利于降低传染病的传播影响力。     

复杂网络上病毒传播的元胞自动机模拟

针对病毒在复杂网络拓扑结构中传播行为的多样性特点,运用元胞自动机模拟病毒传播过程,并采用“易染-感染-免疫”模型和“易染-感染-易染”模型构造元胞自动机模拟方法。实验结果表明,该自动机模型能较好地模拟复杂网络中病毒的传播过程。     

Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.     

传染病在多层星型耦合网络上的资源控制

针对已有传染病传播模型没有考虑到具体的特殊网络结构与资源因素对控制疫情爆发的影响与作用机制,结合双层星型耦合网络与传染病SIS模型,建立了一个离散动态传播模型。该模型利用星型网络的结构特性与平均度概念推导各层感染人口比例关于资源及各种参数的离散方程。理论分析和仿真实验结果表明,多层星型耦合传染病传播网络中存在资源阈值,当节点为叶子节点时,网络存在两个资源阈值,增加资源量投入以抑制传染病传播只在两个资源阈值间有效,此时传染病感染人口比例随着投入资源的增加而减少;当节点为中心节点时,网络中的资源阈值随其他层感染人口比例的增大由两个减少至一个。此外,层间中心节点耦合强度、层间叶子节点耦合强度对疫情的控制效果随着节点所处位置的不同而不同。     

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.     

复杂网络病毒传播元胞自动机模型及研究

为了研究免疫有效时间对复杂网络中病毒传播的影响,基于元胞自动机建立复杂网络不完全免疫的病毒传播模型,并分别在最近邻耦合网络、Erdos-Renyi随机网络、Watts-Strogatz小世界网络和Barabasi-Albert无标度网络中进行仿真研究。结果表明：节点免疫有效时间的增大,能够有效地遏制复杂网络病毒传播范围并增大病毒传播阈值。     

Improved results on synchronisation of delayed complex dynamical networks via sampled-data control

This paper focuses on the synchronisation problem of delayed complex dynamical networks via sampled-data control. A novel input-delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed for the first time, which can make full use of the information on the input delay. To strengthen the combinations of the vectors in the resulting augmented vector, a new zero value equality is founded. Based on the input-delay-dependent LKF and zero value equality, synchronisation criteria are established. In comparison with some existing synchronisation criteria, the criteria in this paper are less conservative. The desired sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the superiorities of proposed results.     

复杂网络健壮社团挖掘算法

提出了一种基于贝叶斯网络的健壮社团挖掘算法,通过对每个普通社团分别构建贝叶斯网络,并根据条件概率表和证据信息进行推理,得到贝叶斯网络中每个节点隶属于健壮社团的后验概率以提取健壮社团。实验结果证明了该方法对健壮社团发现的有效性。     

加权局域网络上的病毒传播行为研究

病毒传播问题的研究一直是国际上科学家所关注的焦点,但是在加权局域网络中的病毒传播研究却是空白。由于实际存在的网络很大一部分是加权局域网络,因此研究了一种特定加权局域网络中的传播行为。采用病毒传播的SI模型,令病毒的传播速度和网络的连接权重正相关。对加权局域网络中病毒传播行为的研究表明：加权局域网络的无标度性质和加权局域世界性质对病毒的传播有深刻的影响。由于加权局域网络能够很好地反应实际世界,因此该研究具有很广的应用背景。     

一种带隔离机制的SIS模型研究

以往的病毒传播模型很少考虑隔离时间对病毒传播结果的影响,根据实际情况提出一个与时间有关的带隔离机制的病毒传播模型,并在BA无标度网络上对其进行模拟,分析试验结果,解释时间机制对病毒传播的影响。     

基于边过滤的代谢网络社团结构分析

社团结构分析有助于理解新陈代谢网络的结构和功能关系,是新陈代谢网络研究领域的一个重要研究主题。然而,直接将复杂网络方法应用到新陈代谢网络中时,很难得到具有实际生物学意义的社团。本文首先构建了高质量人类代谢网络模型的巨强连通体,然后采用一种基于边过滤的技术研究了该巨强连通体,得到的8个主要社团均具备较好的生物学意义。研究结果表明:基于边过滤的技术可用于识别新陈代谢网络中的社团。     

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.     

大规模网络的病毒群体免疫模型

由于计算机和Internet的普及,越来越多的人使用邮件,邮件病毒造成了巨大的损失和严重的破坏。传统的度免疫模型有一定的盲目性,没有考虑感染节点的位置,对整个网络中度高的节点进行免疫。把群体概念引入病毒预防控制领域中,提出群体免疫模型,在不同的病毒感染阶段,采用感染群体免疫或健康群体免疫,在降低节点感染密度的同时,把感染节点控制在一定群体内。度免疫无法将病毒控制在某些群体内,从而使得病毒分散在各个群体;而群体免疫能够将病毒集中到感染群体内部。两种免疫模型需要免疫的节点个数和群体感染比率的差别较大,所以群体免疫是原理上不同于度免疫的新型有效的免疫模型。     

Synchronization of complex dynamical networks with switching topology: A switched system point of view

In this paper, we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view. The synchronization problem is transformed into the stability problem for time-varying switched systems. We address two basic problems: synchronization under arbitrary switching topology, and synchronization via design of switching within a pre-given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection. For the both problems, we first establish synchronization criteria for general connection topology. Then, under the condition of simultaneous triangularization of the connection matrices, a common Lyapunov function (for the first problem) and a single Lyapunov and multiple Lyapunov functions (for the second problem) are systematically constructed respectively by those of several lower-dimensional dynamic systems. In order to achieve synchronization using multiple Lyapunov functions, a stability condition and switching law design method for time-varying switched systems are also presented, which avoid the usual non-increasing condition.