基于混沌和随机共振的微弱信号检测

推导了分数阶线性振子系统响应的一阶稳态矩的频率不变性和相移特性, 并通过理论分析得出, 在随机共振机制下, 分数阶线性振子对系统响应一阶稳态矩的幅值具有放大作用. 构造Duffing混沌振子检测器, 利用混沌系统对参数摄动的敏感性以及对噪声的免疫能力实现弱信号检测. 数值模拟证实, 该方法可以有效地从噪声背景中将微弱正弦信号检测出来, 并且相对传统的混沌检测方法能显著降低信噪比检测门限.     

基于元胞自动机考虑传播延迟的复杂网络病毒传播研究

基于元胞自动机,研究传播延迟对复杂网络病毒传播动力学行为的影响,提出一种新的易染状态-感染状态-易染状态(SIS)传播模型.研究表明,传播延迟的存在显著降低了网络的传播临界值,增强了网络中病毒爆发的危险性.研究还发现,随着传播延迟的增大,病毒的感染程度以及传播速率都明显增大.此外,SIS传播模型不仅能够反映病毒的平均传播趋势,而且可以描述病毒随时间的动态演化过程以及病毒的爆发和消亡等概率事件,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒平均传播趋势的局限性.同时,还给出有效控制网络中病毒传 关键词： 复杂网络 病毒传播 元胞自动机 传播延迟     

基于辟谣机制的时滞谣言传播模型的动力学分析

在社交网络谣言传播模型中,考虑到辟谣机制和时滞效应对网络谣言传播的影响,建立基于辟谣机制和时滞效应的SIR谣言传播模型.利用再生矩阵谱半径方法得到R0;根据二次函数图像特征给出谣言盛行平衡点存在的条件;通过特征值理论和Routh-Hurwitz判据确定无谣言平衡点和谣言盛行平衡点的局部稳定性以及发生Hopf分支的条件;数值仿真结果表明政府和媒体发布的辟谣信息会加快谣言收敛的速度和降低谣言传播者的最大密度.     

在二部无标度网上的两性疾病传播

利用易感-感染-易感(SIS)传播模型研究人类性接触网上的病毒传播.当仅仅考虑异性性接触时,该网络是一个二部的无标度网.对这个网络上的SIS传播模型,通过率方程的方法分析了男性感染率和女性感染率与传染阈值之间的关系,发现女性感染者与男性感染者之比由网络的拓扑和男女感染率之比所确定.这一结果表明性接触网的拓扑对性传染病传播的重要性.最后给出了支持理论结果的数值模拟. 关键词： 性传染病 两性性接触网 无标度网络 二部图     

时滞位移反馈对Helmholtz振子系统的分形侵蚀安全域的控制

对一个Helmoholtz振子系统引入线性时滞位移反馈,研究时滞位移反馈对系统的安全盆侵蚀的控制作用.将Melnikov函数法推广到时滞系统,从而给出时滞受控系统的安全盆的边界分形条件,在此基础上得出了安全盆分形的激励振幅阈值.再以时滞量为变参数,运用四阶Rung-Kutta方法和点映射方法从定量上研究了时滞对受控系统安全盆的影响规律.结果表明在弱反馈下,时滞量的增大能够提高安全盆边界分形的阈值,进而有效地抑制安全盆的分形侵蚀.说明时滞位移反馈是控制系统的安全盆侵蚀的良好方法. 关键词： 安全盆 分形侵蚀 时滞 反馈     

Scaling of the propagation of epidemics in a system of mobile agents

For a two-dimensional system of agents modeled by molecular dynamics, we simulate epidemics spreading, which was recently studied on complex networks. Our resulting network model is time-evolving. We study the transitions to spreading as function of density, temperature and infection time. In addition, we analyze the epidemic threshold associated to a power-law distribution of infection times.     

自适应网络中病毒传播的稳定性和分岔行为研究

自适应复杂网络是以节点状态与拓扑结构之间存在反馈回路为特征的网络. 针对自适应网络病毒传播模型, 利用非线性微分动力学系统研究病毒传播行为; 通过分析非线性系统对应雅可比矩阵的特征方程, 研究其平衡点的局部稳定性和分岔行为, 并推导出各种分岔点的计算公式. 研究表明, 当病毒传播阈值小于病毒存在阈值, 即R₀0^c时, 网络中病毒逐渐消除, 系统的无病毒平衡点是局部渐近稳定的; R₀^c0<1时, 网络出现滞后分岔, 产生双稳态现象, 系统存在稳定的无病毒平衡点、较大稳定的地方病平衡点和较小不稳定的地方病平衡点; R₀>1时, 网络中病毒持续存在, 系统唯一的地方病平衡点是局部渐近稳定的. 研究发现, 系统先后出现了鞍结分岔、跨临界分岔、霍普夫分岔等分岔行为. 最后通过数值仿真验证所得结论的正确性. 关键词： 自适应网络 稳定性 分岔 基本再生数     

Hybrid phase transitions of spreading dynamics in multiplex networks

In this paper, we study the spreading dynamics of social behaviors and focus on heterogenous responses of individuals depending on whether they realize the spreading or not. We model the system with a two-layer multiplex network, in which one layer describes the spreading of social behaviors and the other layer describes the diffusion of the awareness about the spreading. We use the susceptible-infected-susceptible (SIS) model to describe the dynamics of an individual if it is unaware of the spreading of the behavior. While when an individual is aware of the spreading of the social behavior its dynamics will follow the threshold model, in which an individual will adopt a behavior only when the fraction of its neighbors who have adopted the behavior is above a certain threshold. We find that such heterogenous reactions can induce intriguing dynamical properties. The dynamics of the whole network may exhibit hybrid phase transitions with the coexistence of continuous phase transition and bi-stable states. Detailed study of how the diffusion of the awareness influences the spreading dynamics of social behavior is provided. The results are supported by theoretical analysis.     

Modelling crowd–bridge dynamic interaction with a discretely defined crowd

This paper presents a novel method of modelling crowd–bridge interaction using discrete element theory (DET) to model the pedestrian crowd. DET, also known as agent-based modelling, is commonly used in the simulation of pedestrian movement, particularly in cases where building evacuation is critical or potentially problematic. Pedestrians are modelled as individual elements subject to global behavioural rules. In this paper a discrete element crowd model is coupled with a dynamic bridge model in a time-stepping framework. Feedback takes place between both models at each time-step. An additional pedestrian stimulus is introduced that is a function of bridge lateral dynamic behaviour. The pedestrians' relationship with the vibrating bridge as well as the pedestrians around them is thus simulated. The lateral dynamic behaviour of the bridge is modelled as a damped single degree of freedom (SDoF) oscillator. The excitation and mass enhancement of the dynamic system is determined as the sum of individual pedestrian contributions at each time-step. Previous crowd–structure interaction modelling has utilised a continuous hydrodynamic crowd model. Limitations inherent in this modelling approach are identified and results presented that demonstrate the ability of DET to address these limitations. Simulation results demonstrate the model's ability to consider low density traffic flows and inter-subject variability. The emergence of the crowd's velocity–density relationship is also discussed.     

Epidemic spreading in scale-free networks including the effect of individual vigilance

In this paper, we study the epidemic spreading in scale-free networks and propose a new susceptible-infected- recovered (SIR) model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Furthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.     

Epidemic prevalence on random mobile dynamical networks: individual heterogeneity and correlation

In this paper, we extend the susceptible-infected-susceptible (SIS) epidemiological model on a random dynamical network composed of mobile individuals, in which the infection is caused by the collisions between susceptible and infected individuals at the spreading rate proportional to their susceptibilities and infectivities. We analytically study the criticality of spreading dynamics under different distributions of individual susceptibility and infectivity, and numerically verify the cases of power-law and (or) Gaussian distributions. Our findings show that the heterogeneity of individual susceptibility and infectivity increases the epidemic threshold, and the positive correlation of individual susceptibility and infectivity avails to the epidemic prevalence.     

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading inWatts-Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on thespatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.     

Temporal behaviors of epidemic spreading on the scale-free network

Exploring temporal behaviors of the epidemic spreading is of particular importance, in which field an interesting phenomenon of hierarchical spreading cascade has already been demonstrated. By taking into account the effect of density of infected neighbors around an individual in the definition of spreading rate, an infection mechanism modulated by a parameter is introduced in the present paper. Under the mechanism temporal behaviors on the scale-free network are shown to be different, corresponding to different parameters. Three distinct hierarchical spreading modes are typically exhibited. In addition, a novel way to depict the dynamical processes of the epidemic spreading is also developed and some new features are, thus, clearly displayed.     

受迫Holmes-Duffing系统安全域分形及时滞速度反馈控制

以受迫Holmes-Duffing系统为研究对象, 对系统施加时滞速度反馈控制, 研究周期激励引起的系统安全域的分形侵蚀及时滞速度反馈对分形侵蚀安全盆的控制作用. 利用Melnikov函数法给出时滞受控系统的安全盆的边界分形条件. 再以时滞量为变参数, 运用四阶Runge-Kutta方法和点映射方法数值研究了时滞对受控系统安全盆的影响规律. 结果表明在弱反馈下, 时滞量的增大能够提高安全盆边界分形的阈值, 从而抑制安全盆的分形侵蚀. 说明时滞速度反馈能够有效抑制系统的安全盆侵蚀.     

异质自适应网络中的核心-边缘结构及其对疾病传播的抑制作用

节点属性异质自适应网络中疾病传播的研究表明节点属性异质性可以很大程度上增大传播阈值, 并且自组织形成一个更鲁棒的度异质网络结构. 本文从数值模拟方面研究鲁棒的度分布异质结构的自组织形成过程, 分析发现核心-边缘结构的形成才是导致传播阈值增大的根本原因. 鉴于此, 提出一种重连策略, 能够促进核心-边缘结构的形成, 从而达到增大传播阈值的目的. 这不仅有助于深入认识节点属性异质自适应网络中的流行病传播过程, 而且为疾病传播控制策略的提出提供了新思路.     

用静电探针反馈控制KT—5C托卡马克边缘湍流

在ＫＴ－５Ｃ托卡马克上，利用两组边缘静电探针分析作为控制探针和探测探针进行了反馈控制边缘湍流的实验，在适当的回路增益下的，当系统相移为９０°时，反馈使湍动幅度明显地抑制，电子密度和电子温度扰劝均降低了约２５％，横向粒子输运通量也相应地降低了２５％，而相移为０°，１８０°和－９０°的反馈却使湍动幅度增强，这显示反馈是基于一种非线性机制而作用于湍动的，在一定意义上，这正体现了湍流本身的非线性特征。     

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介绍了HL-2A等离子体密度反馈控制系统的设计和实现。从密度反馈控制系统的设计原理、硬件设计和软件设计几方面,论述了等离子体密度反馈系统在HL-2A装置上的实现。实验证明,该系统实现了维持稳定可靠的密度波形的要求。     

多关系网络上的流行病传播动力学研究

多关系网络已经吸引了许多人的注意, 目前的研究主要涉及其拓扑结构及其演化的分析、 不同类型关系的挖掘、重叠社区的检测、级联失效动力学等. 然而,多关系网络上流行病传播的研究还相对较少. 由此提出一种双关系网络模型(工作-朋友关系网), 研究多关系对于流行病传播动力学行为的影响. 在全接触模式下, 多关系的存在会显著降低网络中的爆发阈值, 使得疾病更容易流行而难以控制. 对比ER (Erdös-Rènyi), WS (Watts-Strogatz), BA (Barabási-Albert)三种网络, 由于结构异质性的差异, WS网络受到的影响最大, ER网络次之, BA网络最小. 有趣的是, 其爆发阈值的相对变化大小与网络结构无关. 在单点接触模式下, 增加强关系的权重将显著提升爆发阈值, 降低感染密度; 随着强关系的比例变化将出现最优值现象: 极大的爆发阈值和极小的感染密度. 随着强关系的边权增加, 达到最优值的边比例将减少. 更为有趣的是, 三个网络中优值出现的位置几乎一致, 独立于网络结构. 这一研究不但有助于理解多关系网络上的病毒传播过程, 也为多关系网络研究提供了一个新的视角. 关键词： 多关系网络 流行病传播 接触模式 爆发阈值     

Equilibrium of a two-route system with delayed information feedback strategies

In intelligent transport system, some advanced information feedback strategies have been developed to reduce the oscillations and enhance the capacity on the road level. However, seldom strategies have considered the information delay and user equilibrium (UE) objective. Here, a derivative cost feedback strategy (DCFS) is proposed to reduce the influence of the delay, based on the UE principle. The simulation results show that in both no-delay and delay information cases, DCFS are the best and can make the system reaching the UE. Because DCFS can predict the trend of the travel cost.     

Dynamics of emotional contagion in dense pedestrian crowds

In places with high-density pedestrian movements, irrational emotions can quickly spread out under emergency, which may eventually lead to asphyxiation and crushing. It was noticed that a pedestrian's emotion in crowd would change as a result of the influence from other pedestrians. Thus, to explore the dynamics of emotion contagion process in dense pedestrians, two types of pedestrian emotions, i.e., negative and positive have been identified. Taking into account the emotional transit of a pedestrian, a crowd movement model is established in the present paper. We simulate pedestrian movement in a region with periodic boundary condition to study the dynamics of emotional contagion in dense crowds. Influences of the initial negative pedestrian proportion, pedestrian crowd density, emotion influence radius, and dose factor on the transition of overall crowd emotion state have been investigated. We expect this study could provide theoretical suggestions for crowd management.