基于加权局域世界的金融网络演化模型研究

在加权局域世界网络模型的基础上,文章将复杂网络与金融系统相结合,提出一种新局域世界的加权金融网络模型.其主要思想是在加权局域世界网络中引入了服从指数分布的增长方式和双向择优选择的连边方式.利用平均场理论和仿真模拟得到网络节点度、强度和权值都服从幂律分布,其分布指数与所取参数有关.通过网络拓扑性质的研究和沪市A股股票数据的实证研究,发现该金融网络模型具有层次结构和异配特性,与实际网络具有相似的拓扑结构.     

基于复杂网络的邮件病毒的传播模型

本文以电子邮件病毒为例，通过构建改进的SEIR病毒传播模型，并结合更符合实际的复杂网络与人际关系对病毒的传播特性进行深入研究。从用户的主观与客观等多种角度研究了有效拉制病毒在网络中快速传播的方式．理论分析及仿真实验表明，通过对实际生活中某些参数的控制，能有效遏制邮件病毒在网络中的传播．‘     

木马病毒传播数学模型研究

随着网络行为同社会行为联系的进一步密切,网络攻击的最终目的越来越多地落在获取具体的经济意义上.病毒制造者和传播者在巨大利益的驱使下,利用木马技术进行各种网络盗窃、诈骗活动.计算机网络病毒传播模型是研究计算机网络病毒的手段和工具之一,根据木马病毒的特点,建立了木马病毒的数学模型,研究了影响病毒传播的参数及对应措施.     

复杂金融网络收益率加权和的不变性研究

对包含两个子网络的复杂金融网络进行了分析,研究了网络中各节点收益率与资金流通量之间的关系.通过建立数学模型,证明了网络中各节点收益率加权和的不变性.     

探讨几类具有完全图核心的网络模型的优美性

在复杂网络研究中,人们需要建立网络模型,无标度图就是这样的一种网络模型.我们发现具有完全图核心的网络模型可以演变成无标度图.具有完全图核心的几种网络模型的优美性得到研究.     

寨卡病毒传播潜力与控制策略有效性分析

目前寨卡病毒已在超过65个国家和地区传播, 为了估计新加坡寨卡病毒的传播潜力和有关控制策略的有效性, 首先采用经典的传染病模型并结合累计报告病例数, 借助最小二乘法和MCMC方法进行模型参数估计, 寻求拟合累计病例数最佳的参数集合及其相应的置信区间.进而根据再生矩阵法求得的基本再生数公式,得到了新加坡寨卡爆发的阈值参数R₀的估计值和置信区间, 通过对比分析验证了新加坡寨卡病毒传播基本再生数的可靠性.之后, 分析了累计病例数对各个关键参数的敏感性, 探讨针对寨卡病毒传播控制策略的有效性.结果表明: 在对新加坡寨卡病毒的控制中, 需要通过增加检疫次数和检疫率、对患者进行隔离以及有效地灭蚊, 并且通过减少疫区的游客数量达到控制疫情的效果.     

异质网络上几类传染病模型及其全局动力学分析

随着复杂网络不断渗入众多学科领域,经典的传染病模型无法精确描述现实社会的接触网络,因此,利用合理的复杂网络模型描绘各种各样的复杂系统成为复杂性科学领域的研究前沿和热点.综述介绍了一类复杂网络传播动力学几种改进的异质网络模型及其全局动力学分析方法.     

高温超导体的顺磁Meissner效应——II.局域磁矩唯象模型

在前文中提出的实验设计思想 ,对二十几个不同类型的样品进行了系统的研究 .在此基础上提出了一个局域磁矩唯象模型 .通过对实验数据的拟合 ,首次给出了局域磁矩的大小、浓度及其分布 .进而对局域磁矩大小与样品颗粒尺寸、颗粒间的弱连接的关系 ,局域磁矩之间以及局域磁矩与超导抗磁磁矩之间的相互作用等问题进行了讨论 .实验结果表明 ,由局域磁矩模型得到的结论是普遍适用的     

基于超图的超网络研究综述

超网络是一般网络的一类自然推广。超网络的研究将会有助于理解“复杂系统之所以复杂”这一极其重要的问题。现实世界中,很多复杂的系统都可以用超网络描述。超网络分为基于网络的超网络与基于超图的超网络。本文主要介绍的是基于超图的超网络,首先对超图理论进行描述,然后对基于超图的超网络进行分析,接着提出了基于超图的超网络和多层超网络的转换及实例并提出了基于超图的超网络演化模型。本文最后对超网络今后的研究方向进行了探讨,其中,超网络的指标构建、动力学研究、链路预测、应用等方面还有待于深入研究。     

广义加权网络演化模型

在复杂网络BBV演化模型的基础上,采用新的赋权方式构建广义加权网络FBBV动态演化模型,给出FBBV模型的演化算法,然后对FBBV模型的性质进行理论推导,给出点权、边权的演化公式和点权、度和边权的分布规律.最后对FBBV模型进行了数值模拟,模拟的结果和理论推导结果一致.     

群体行为的异质节点复杂网络传播

当遭遇突发的公共社会安全事件时,具有负面影响的应激行为可能迅速在社会范围内传播扩散,形成群体行为.虽然一些复杂网络的传染模型能够对此进行刻画,但更为符合实际的是行为群体根据一些特性可能划分为不同的亚群体,为此将建立异质节点SIS复杂网络模型.此后,依据亚群体的有效传播率与度分布无关、正相关和负相关三种情形,分别研究了群体行为在异质节点的小世界网络传播特性,及异质节点的无标度网络传播特性.无论是异质节点的小世界网络模型还是异质节点的无标度网络模型,平均场动力学分析和计算机模拟结果显示,当亚群体的传播率与度分布呈正相关时,群体行为的传播会出现放大相应;反之,当亚群体的传播率与度分布成负相关时,群体行为的传播会出现抑制效应.但以上的两种效应在离散性更强的无标度网络上更为明显.     

病毒传播的动态分析

结合最新病毒传播的研究工作,建立了一系列微观病毒传播系统,并对动态系统作了简单的分析,是对宏观疾病传播的内在规律的描述和研究,有利于疾病发展趋势的预测和最优化控制策略的研究.     

A fractional order HIV-TB coinfection model with nonsingular Mittag-Leffler Law

The biological models for the study of human immunodeficiency virus (HIV) and its advanced stage acquired immune deficiency syndrome (AIDS) have been widely studied in last two decades. HIV virus can be transmitted by different means including blood, semen, preseminal fluid, rectal fluid, breast milk, and many more. Therefore, initiating HIV treatment with the TB treatment development has some advantages including less HIV-related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of a large pill encumbrance. It has been analyzed that patients with HIV have more weaker immune system and are susceptible to infections, for example, tuberculosis (TB). Keeping the importance of the HIV models, we are interested to consider an analysis of HIV-TB coinfected model in the Atangana-Baleanu fractional differential form. The model is studied for the existence, uniqueness of solution, Hyers-Ulam (HU) stability and numerical simulations with assumption of specific parameters.     

A propagation model with defensive measures for PLC-PC worms in industrial networks

Programmable logic controllers (PLCs) are important components of industrial control systems (ICSs), which are digital electronic devices with microprocessors and lack network security considerations. With the explosion of cyber-attacks on the ICS network, the concept of the worm known as PLC-PC worm that can spread between the Internet and ICS network has attracted a great deal of attention. In this paper, for the first time, we propose a propagation model to explore the spread behavior of PLC-PC worms across the PLC-PC coupled network. Theoretical analysis of the model shows the disease-free and endemic equilibriums of the network with defensive measures. And the stability of the model is examined by an epidemic threshold value. Several numerical and simulation experiments are presented to illustrate the analysis. Based on the results, some ideas for restraining the spread of PLC-PC worms or reducing the security threats of the ICS network are suggested.     

Complex dynamics of epidemic models on adaptive networks

There has been a substantial amount of well mixing epidemic models devoted to characterizing the observed complex phenomena (such as bistability, hysteresis, oscillations, etc.) during the transmission of many infectious diseases. A comprehensive explanation of these phenomena by epidemic models on complex networks is still lacking. In this paper we study epidemic dynamics in an adaptive network proposed by Gross et al., where the susceptibles are able to avoid contact with the infectious by rewiring their network connections. Such rewiring of the local connections changes the topology of the network, and inevitably has a profound effect on the transmission of the disease, which in turn influences the rewiring process. We rigorously prove that the adaptive epidemic model investigated in this paper exhibits degenerate Hopf bifurcation, homoclinic bifurcation and Bogdanov–Takens bifurcation. Our study shows that adaptive behaviors during an epidemic may induce complex dynamics of disease transmission, including bistability, transient and sustained oscillations, which contrast sharply to the dynamics of classical network models. Our results yield deeper insights into the interplay between topology of networks and the dynamics of disease transmission on networks.     

基于人工免疫网络的药代动力学参数优化方法

提出了基于人工免疫网络优化药代动力学参数的PKAIN算法．新增的分组并发单纯形变异用以提高人工免疫网络的局部搜索能力．通过PKAIN人工免疫网络中网络细胞的进化得到给定药代动力学模型的一组优化参数．应用Laplace变换求解瑞芬太尼(remifentanil)及其代谢产物瑞芬太尼酸的联合代谢动力学模型的微分方程组,通过PKAIN算法优化导出房室模型参数A·D2实验表明,对伴有轻度肾损伤病人可以应用二室模型描述瑞芬太尼酸的药代动力学特征．     

Interest point detection in images using complex network analysis

This paper presents a new application of complex network theory and tools to digital image analysis and computer vision problems in order to detect interest points in digital images. We associate a weighted geometrical and fast computable complex network to each image and then we propose two different methods to locate these feature points based on both local and global (spectral) centrality measures of the corresponding network.     

Resource allocation in state-dependent emergency evacuation networks

Most of the previous studies on the Emergency Evacuation Problem (EEP) assume that the length and widths of the circulation spaces are fixed. This assumption is only true if one is evaluating facilities that are already built. However, when designing the network for the first time, the size of the circulation space is not known to the designer, in fact it is one of several design parameters. After the routes have been established, it seems that the next logical question is to find out whether or not the system circulation spaces are capable of accommodating the traffic for both normal circulation and in an emergency. The problem of designing emergency evacuation networks is very complex and it is only recently that queueing networks are now being used to model this problem. Recent advances include state-dependent queueing network models that incorporate the mean value analysis algorithm to capture the non-linearities in the problem. We extend these models by incorporating the mean value analysis algorithm within Powell's derivative free unconstrained optimization algorithm. The effect of varying circulation widths on throughput will be discussed and a methodology for solving the resource allocation problem is proposed and demonstrated on several examples. The computational experience of the new methodology illustrates its usefulness in network design problems.     

Effects of the killing rate on global bifurcation in an oncolytic-virus system with tumors

Oncologists and virologist are quite concerned about many kinds of issues related to tumor-virus dynamics in different virus models. Since the virus invasive behavior emerges from combined effects of tumor cell proliferation, migration and cell-microenvironment interactions, it has been recognized as a complex process and usually simulated by nonlinear differential systems. In this paper, a nonlinear differential model for tumor-virus dynamics is investigated mathematically. We first give a priori estimates for positive steady-states and analyze the stability of the positive constant solution. And then, based on these, we mainly discuss effects of the rate of killing infected cells on the bifurcation solution emanating from the positive constant solution by taking the killing rate as the bifurcation parameter.     

A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.