复杂网络的随机刻画和演化规律

从4个方面来介绍复杂网络的随机刻画和演化规律: 经典模型和网络特性;实证研究和建模进展; 分析网络的理论方法; 网络社会中人类行为.着重说明好的网络模型如何反映实际网络的演化机理和网络各种性能测度如何刻画实际网络的特性.基于复杂网络演化的随机性和动态性特点, 讨论现有分析网络的理论方法,以及可能的发展趋势. 再根据近期的研究发现,评述网络社会中人类动力学的建模及其对网络特性的影响.      

复杂网络上的博弈

博弈理论在社会、经济、生物以及生态等系统中存在着广泛的应用,复杂网络理论则是研究复杂系统全新而有力的工具,因此将博弈理论与复杂网络理论相结合成为研究复杂系统一个新的热点.概述国内外当前关于复杂网络上博弈动力学的研究情况和发展动态,包括基本的博弈模型、主要关注的问题、以及网络结构和博弈动力学的相互作用等,最后探讨进一步的研究课题.      

复杂网络上集群行为与自旋模型

复杂系统中的集群行为(collective behavior)是复杂系统涌现性的重要表现之一, 它通过微观个体之间的相互作用, 在宏观上表现出一定的时空或功能有序结构．已有研究表明, 个体之间相互作用的网络结构对复杂系统的集群行为有重要影响．基于复杂网络上的自旋模型, 介绍了复杂网络上的集群行为的部分研究进展． 首先简要介绍了自旋模型的相变现象以及网络结构对相变行为的影响; 其次, 介绍了以自旋模型为基础应用到社会经济等领域中的工作, 包括舆论形成、羊群效应以及分隔现象(segregation)等, 尤其关注网络结构对集群行为的影响, 最后介绍了基于自旋模型的网络社团划分方法．对进一步的发展方向进行了初步的讨论．     

复杂网络的同步: 理论、方法、应用与展望

复杂网络随处可见, 如互联网、电力网络、商业网络、生物神经网络、社会关系网等. 这些复杂网络与我们的生活息息相关, 对它们的深入研究不但会促进许多重要科学分支的发展而且可能引起人类社会生活方式的根本变革. 同步是自然界中广泛存在的一类非常重要的非线性现象, 复杂网络展示了丰富多彩的网络同步现象. 在过去10年里, 不同研究领域的学者从不同的角度广泛而深入地开展了复杂网络同步的研究. 本文简要的回顾国内外过去10年在复杂网络同步领域的主要研究进展, 包括理论、方法、应用与展望, 试图推进国内复杂网络同步的研究.      

基于脉冲控制下的复杂时滞动力网络的鲁棒同步

近年来复杂网络已经引起了科学和工程技术等各个领域的广泛关注,尤其是复杂网络中的非线性动力学行为,以及网络的拓扑结构如何影响它的动力学行为的研究,已成为当前一项极其重要的战略课题.本文主要讨论基于脉冲控制下复杂时滞动力网络的同步动力学,应用时滞动力系统的脉冲控制理论,给出了复杂时滞动力网络的一些简单而又一般的鲁棒同步化准则,这些准则能够提供一个新的和有效的控制方法来同步一个任意给定的时滞动力网络到一个期望的同步态,进一步地将所获得的结果应用到由混沌FHN神经元振子为动力节点所构成的一个具有近邻耦合结构的复杂动力网络,数值模拟表明了所获理论结果的正确性和控制方法的有效性.     

血细胞生成的系统动力学研究进展

造血系统是人体中复杂的调控系统, 包括复杂的造血器官和各种血液细胞的增生、分化、成熟、死亡等过程和对这些过程的反馈控制, 是典型的非线性时滞动力系统. 血细胞生成过程的失调可以引起很多动态血液病. 血细胞生成的系统动力学研究对于人们了解和治疗这些血液病有重大意义. 本文从造血系统的基本知识、常见动态血液病的临床表现及其动力学特征、理论模型的建立和对模型的动力学分析等方面综述血细胞生成的系统动力学研究进展.     

延时神经网络混沌现象的研究

本文研究一个具有部分延时性能的三个神经元的不对称神经网络系统的动力学行为，讨论了当控制参数变化时网络呈现的各种现象，计算了李雅普人指数研究了阵发混沌现象，最后讨论了全延时神经网络的吸引子。     

《系统生物学—建模,分析,模拟》书评

生命活动属于最复杂的自然界现象。近代生物学研究已从以实验观察为主的方式逐步发展为与生命体的机理性分析密切结合,并且由生物器官组织的宏观形态和表型向生物细胞和分子的微观行为和演变进行深入探讨。随着生物科学实验技术和方法的飞速进步,人们对生物大分子、基因和蛋白质、生物膜的结构和功能等的研究已经积累了相当丰富的知识。由于生命现象都是生物复杂大系统的综合行为的结果,我们必须把生物系统作为一个整体来研究,从系统论的角度进一步探讨细胞的信息、生长、发育、分化、代谢等动态过程以及生物有机体的功能,而不仅把研究重点放在单个的基因, 蛋白质或者器官上。系统生物学就是这样一门研究生物系统的内部组分结构, 以及在各种内、外部条件下这些组分的相互作用和演化规律的学科,是生命科学的一个前沿领域。目前重点是在分子层次上开展对生命现象（例如遗传基因、蛋白质、重大疾病等）的过程和机制的研究,生物化学反应（包括蛋白质—蛋白质相互作用、DNA—蛋白质相互作用等）和生物网络（包括基因网、蛋白质相互作用网、信号转导网、代谢网等）行为在其中起着重要作用。大量的系统生物学研究对象是动态的和随机的,涉及不同的时空尺度下复杂非线性动力学与控制问题。      

ADVANCES AND OUTLOOK IN TURBULENT RAYLEIGH-BENARD CONVECTION

对流现象广泛存在于恒星和行星里.在地球上,对流现象在诸如大气、海洋、地核和地幔等众多动力学系统中起着重要作用.Rayleigh-Bénard（RB）湍流热对流系统是从这些复杂的自然现象中抽象出来的研究对流问题的经典流体力学模型.本文主要从湍流传热、羽流、大尺度流动结构、速度和温度脉动的小尺度统计和非传统RB对流等几个方面着重评述近年来RB对流的若干研究新进展,并对今后的研究做出展望.     

Rayleigh-Bénard湍流热对流研究的进展、现状及展望

对流现象广泛存在于恒星和行星里.在地球上,对流现象在诸如大气、海洋、地核和地幔等众多动力学系统中起着重要作用.Rayleigh-Bénard(RB)湍流热对流系统是从这些复杂的自然现象中抽象出来的研究对流问题的经典流体力学模型.本文主要从湍流传热、羽流、大尺度流动结构、速度和温度脉动的小尺度统计和非传统RB对流等几个方面着重评述近年来RB对流的若干研究新进展,并对今后的研究做出展望.     

Dynamical model and control of a small-world network with memory

This paper proposes a dynamical model of influence volume of small-world-network with memory to investigate the effects of multiple delays on network dynamics. We calculate the influence volume covered by the spreading quantity, discuss the effect of finite size on the network dynamics, and then give the saturate time. The dynamical control is also investigated by introducing the delayed state feedback to simulate the adaptivity of network. With properly chosen delay and gain in feedback path, the controlled model may have stable equilibrium, periodic solution, quasi-periodic solution, or a complex chaotic attractor from a sequence of period-doubling bifurcations. It shows delayed feedback control may find important applications in the management and dynamical control of complex networks.     

The chaotic dynamics of the social behavior selection networks in crowd simulation

This paper researches the nonlinear dynamics of the behavior selection networks (BSN) model by virtue of which we can understand the origin of flocking behaviors in social networks. To commentate the notion of BSN, this article introduces a social behavior selection model for evolutionary dynamics of behaviors in social networks that exhibits a rich set of emergent behaviors of evolution. For behavioral networks with different complex networks topology, we analyze the nonlinear dynamics including the chaotic dynamics by the numerical simulation tools. With changing the topological structure, the behavioral networks behave affluent dynamical phenomena. Lastly, we draw the conclusion and paste the prospection about the networks model.     

An SIR model with infection delay and propagation vector in complex networks

Based on the SIR (Susceptible-Infected-Removed) model, we propose a novel epidemic model to investigate the impact of infection delay and propagation vector on the spreading behaviors in complex networks. Mean-field approximations and extensive numerical simulations indicate that the infection delay and propagation vector can largely reduce the critical threshold and promote the outbreak of epidemics, and even lead to the case that the infectious diseases transform from the disease-free state to endemic one. The current results are greatly instructive for us to further understand the epidemic spreading and design some effective prevention and containment strategies to fight the epidemics.     

Adaptive synchronization of T-S fuzzy complex networks with time-varying delays via the pinning control method

In this paper, the synchronization of Takagi–Sugeno (T-S) fuzzy complex networks with time-varying delays and adaptive coupling weights is studied. Using the pinning control and adaptive feedback strategy, a new general class of complex networks with fuzzy logic is proposed and its synchronization is investigated in terms of linear matrix inequalities (LMIs). The adaptive update law of coupling weight is only related to the dynamical behaviors of directly connected nodes. Based on the Lyapunov stability theory, it is proven that the synchronization of the addressed network can be achieved under those control strategies. Finally, two numerical examples are given to verify the effectiveness of our theoretical results.     

Complexity of triopoly price game in Chinese cold rolled steel market

This paper considers a Bertrand model based on nonlinear demand functions which are closer to reality and different from previous studies. We apply the model into Chinese cold rolled steel market and study game process of triopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Simulations show complex dynamical behaviors of the system. The results illustrate that altering the relevant parameters of system can affect the stability of Nash equilibrium point and cause chaos to occur, and the complex dynamical behaviors will disappear by parameters control method. The results have an important theoretical and practical significance to Chinese cold rolled steel market.     

规范形网络中的混沌吸引子

讨论多余维Hopf分叉三阶规范形的普适开折形成的网络更进一步的复杂动力学行为．通过对余维二Hopf分叉的规范形网络多级分叉的分析，发现在参数空间的某个区域会出现二环面，将S形非线性加入规范形网络，在出现二环面的区域内可以出现混沌．本文给出了该混沌吸引子的相图及其二阶Poincare映射的图景．由这些图可以看到该混沌吸引子具有非常奇妙的形态：某些二阶Poincare映射像一只逼真的蝴蝶．     

人工神经网络非线性动力学及应用

综述神经网络系统非线性动力学行为及其与网络性能的联系和在科学和工程中的应用；讨论了神经网络的权值动力学系统和状态动力学系统的动态过程，神经网络的稳定性和鲁棒稳定性，高阶关联网络的性能、张量描述、吸引性和复杂性，神经网络设计和综合的分叉理论；说明了神经网络动力学分析的意义和重要性．     

Partially unstable attractors in networks of forced integrate-and-fire oscillators

The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basin can arise, where almost every point on the attractor is locally transversely repelling. Herewith we report our discovery of a class of attractors: partially unstable attractors, in pulse-coupled integrate-and-fire networks subject to a periodic forcing. The defining feature of such an attractor is that it can simultaneously possess locally stable and unstable sets, both of positive measure. Exploiting the structure of the key dynamical events in the network, we develop a symbolic analysis that can fully explain the emergence of the partially unstable attractors. To our knowledge, such exotic attractors have not been reported previously, and we expect them to arise commonly in biological networks whose dynamics are governed by pulse (or spike) generation.     

Noise-induced outer synchronization between two different complex dynamical networks

In this paper, based on the theory of stochastic differential equations, we study the outer synchronization between two different complex dynamical networks with noise coupling. The theoretical result shows that two different complex networks can achieve generalized outer synchronization only with white-noise-based coupling. Numerical examples further verify the effectiveness and feasibility of the theoretical results. Numerical evidence shows that the synchronization rate is proportional to the noise intensity.