关于一个扰动非线性薛定谔方程的注记

本文讨论了一个扰动非线性薛定谔方程对于Ｓｔｏｋｅｓ波的一类同宿轨道，证明了这类轨道是不存在的。     

具有不同耦合强度且带有时滞的振子网络上的同步

本文研究了具有不同耦合强度且带有时滞的振子网络上的同步问题．我们给出了该网络同步状态的稳定性准则，证实了其同步状态的稳定性与网络的拓扑性无关．最后，通过数值模拟验证了我们的理论结果．     

传播动力学模型回顾与展望

传播动力学模型主要包括传染病动力学模型、计算机病毒传播模型以及谣言传播模型.首先从传染病动力学模型入手,分别介绍均匀混合传染病动力学模型和网络动力学模型;然后介绍计算机病毒传播模型以及谣言传播模型,并与传染病模型进行对比.最后作了总结与展望.     

耦合动力系统的Conley指标

从Hessian矩阵入手,研究了几种有限网络上动力系统的两种孤立不变集的Conley指标.对于网络节点仅具有单个状态参量时,分析了在线性耦合关系和非线性耦合关系下的全连接网络(全耦合网络)、最近邻网络和任意连接网络上流的孤立不动点的Conley指标与单个节点状态流的孤立不动点的Conley指标的关系;对于节点具有双状态参量和孤立节点不变集为极限环时,给出了在一定耦合条件下,文中所定义的映射F(s)的C0nley指标与节点状态积流的Conley指标的关系.     

Adaptive Function Projective Synchronization of Discrete Chaotic Systems with Unknown Parameters

Adaptive function projective synchronization of discrete-time chaotic systems with unknown parameters is considered. Based on the contraction mapping theorem, proper controllers and estimators are designed. Illustrative examples are provided to show the effectiveness of this method.     

Epidemic thresholds in a heterogenous population with competing strains

Among many epidemic models,one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper,we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach,we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.     

Topology Identification of General Dynamical Network with Distributed Time Delays

Genera/dynamical networks with distributed time delays are studied. The topology of the networks are viewed as unknown parameters, which need to be identified. Some auxiliary systems （also called the network estimators） are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied in designing these network estimators. Based on linear matrix inequalities and the Lyapunov function method, the sufficient condition for the achievement of topology identification is obtained. This method can also better monitor the switching topology of dynamical networks. Illustrative examples are provided to show the effectiveness of this method.     

一般符号动力系统的浑沌性态*

本文将符号动力系统理论推广到一般的情况,讨论当X为可分度量空间时,一般符号动力系统(∑(X),σ)及其特例的浑沌性质及应用.     

Chaotic behaviour of the general symbolic dynamics

This paper extends symbolic dynamics to general cases. Some chaotic properties and applications of the general symbolic dynamics (∑(X),σ) and its special cases are discussed, where X is a separable metric space.     

Dynamical behaviour of an epidemic on complex networks with population mobility

In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population's mobility on the epidemic spreading. In view of the population's mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.