Effects of Variant Rates and Noise on Epidemic Spreading

We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic spreading.The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution.However,the noise parameter which is taken from a given distribution,i.e.Gaussian can describe the fluctuations of the infection and recovery rates.The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.

Message Spreading and Forget-Remember Mechanism on a Scale-Free Network

我们学习消息在一个没有规模的网络上传播，由介绍新奇忘记记得机制。消息，能指电子邮件的一个一般术语，新闻，谣言或疾病，等等，能被它的持有者忘记并且记得。消息被忘记并且记得的方法被 forget 管理并且分别地记得功能， F 和 R。F 和 R 是有关个人的家的历史时间 t 的功能以前的状态，也就是是活跃的(与消息) 或不活跃(没有消息) 。我们以传播能是有效的低传播率的系统的模拟表演被相应参数首先为 F 和 R 决定。

The Fractal Dimensions of Complex Networks

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.

Maximum Path Information and Fokker-Planck Equation

我们在场从 Maupertuis 的最少的行动的原则的归纳直接导出异常散开的非线性的佛克普朗克常数(FP ) 方程的一个严密方法由王求婚了[混乱， Solitons 和分数维图形 23 (2005 ) 1253 ] 为在 Markovian 演变的光滑或伪光滑的不规则的动力学过程。获得的 FP 方程可以拿二种不同却相等的形式。散开常数可以取决于两 q，这也被发现(Tsallis 熵的索引[J。Stat。Phys。52 (1988 ) 479 ] 并且时间 t ) 。

Long Division Unites or Long Union Divides:a Model for Social Network Evolution

A remarkable phenomenon in the time evolution of many networks such as cultural,political,national and economic systems is the recurrent transition between the states of union and the division of nodes.We propose a phenomenological modeling,inspired by the maxim"long union divides and long division unites"to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events.The nodes are endowed with quantities such as identity,ingredient,richness(power),openness(connections),age,distance,and interaction,which determine collectively the evolution in a probabilistic way.Depending on a tunable parameter,the time evolution of this model is mainly an alternative domination of union or division state,with a possible state of final union dominated by one single node.

Emergence of Community Structure in the Adaptive Social Networks

In this paper,we propose a simple model of opinion dynamics to construct social networks,based on the algorithm of link rewiring of local attachment(RLA)and global attachment(RGA).Generality,the system does reach a steady state where all individuals'opinion and the complex network structure are fixed.The RGA enhances the ability of consensus of opinion formation.Furthermore,by tuning a model parameter p,which governs the proportion of RLA and RGA,we find the formation of hierarchical structure in the social networks for p>p_(c).Here,p_(c) is related to the complex network size N and the minimal coordination number 2K.The model also reproduces many features of large social networks,including the“weak links”property.

Opinion Dynamics of Sznajd Model on Small-World Network

The society structure plays an important role in shaping the attitudes,beliefs and public opinion.For studying the role of the society structure in opinion dynamics,we analyze the Sznajd model on small-world network formed by adding shortcuts in a lattice consisting of N nodes arranged in a ring and on two-dimensional(2-D)regular lattice.Through computer simulation,we find that there exists a pseudo-phase transition from the coexistence state forφ<φ_(c) to the consensus state forφ>φ_(c),whereφ_(c) is some threshold for the shortcut densityφ,which is dependent of the complex network topology and the dimensionality of complex networks.Our observations indicate the dependence of the opinion dynamics on the complex system topology.

Effects of Complex System Topology on the Bak-Sneppen Evolution Model

In this paper, we investigate by numerical simulations the Bak-Sneppenmodel (BSM) for biological evolution on scale-free networks (SFNs) with various degree exponents γ. We find that the punctuated equilibrium is rather robust with respect to the network topology. Furthermore, we analyze the evolution of the criticalaverage fitness h fi ∗ and the exponent τ of h fi 0 avalanche as a function of α (i.e., the degree exponent γ). Our observations indicate the dependence of evolutionary dynamicsof BSM on the complex biosystem topology.

Continuous Opinion Dynamics in Complex Networks

Many realistic social networks share some universal characteristic properties,such as the small-world effects and the heterogeneous distribution of connectivity degree,which affect the dynamics in society system,especially the opinion dynamics in society.To see this,we study the opinion dynamics of the Improved Deffuant Model(IDM)in complex networks.When the two opinions differ by less than the confidence parameterǫ(0<ǫ<1),each opinion moves partly in the direction of the other with the convergence parameterµ,which is a function of the opposite’s degree k;otherwise,the two refuse to discuss and no opinion is changed.We analyze the evolution of the steady opinion s∗as a function of the confidence parameterǫ,the relation between the minority steady opinion smin∗and the individual connectivity k,and find some interesting results that show the dependence of the opinion dynamics on the confidence parameter and on the system topology.This study provides a new perspective and tools to understand the effects of complex system topology on opinion dynamics.