移动环境下网络病毒传播模型及其稳定性研究

考虑网络节点的随机移动, 基于平均场理论 提出一个移动环境下网络病毒传播的数学模型, 利用微分动力学系统理论研究了病毒传播行为. 研究表明, 当病毒基本再生数R₀ ≤ 1时, 网络中病毒逐渐消除, 系统的无病毒平衡点全局渐进稳定; 当R₀ > 1时, 网络中病毒持续存在, 系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.     

无标度网络中最大传染能力限定的病毒传播问题研究

传统的病毒传播模型在无限大无标度网络上不存在病毒传播阈值,即无论病毒的传播速率多么低,病毒始终能够在网络中传播.但研究发现,这个结论是在网络中存在超级传染者的假设下得到的,然而许多真实的无标度网络中并不存在超级传染者.因此,文章提出了一个最大传染能力限定的病毒传播模型,并从理论上证明了在最大传染能力限定的无限大无标度网络上,病毒传播阈值是存在的;同时,也分析了最大传染能力限定下非零传播阈值与有限规模网络下非零传播阈值的本质区别,并解释了为什么人们总是认为传统病毒传播模型对许多真实网络病毒感染程度估计过高的 关键词： 无标度网络 最大传染能力 传播阈值 感染程度     

非线性传送带系统的复杂分岔

讨论了一类单自由度非线性传送带系统. 首先通过分段光滑动力系统理论得出系统滑动区域的解析分析和平衡点存在性条件; 其次利用数值方法, 对系统几种类型的周期轨道进行单参数和双参数延拓, 得到系统的余维一滑动分岔曲线和若干余维二滑动分岔点, 以及系统在参数空间中的全局分岔图. 通过对系统分岔行为的研究, 反映出传送带速度和摩擦力振幅对系统动力学行为有较大影响, 揭示了非线性传送带系统的复杂动力学现象. 关键词： 传送带系统 滑动分岔 周期运动     

一种基于元胞自动机的自适应网络病毒传播模型

自适应网络是节点动力学和网络动力学相互作用和反馈的演化网络. 基于元胞自动机建立自适应网络中易感-感染-易感(susceptible-infected-susceptible)的病毒传播模型,研究节点为了规避病毒传播所采取的多种网络重连规则对病毒传播及网络统计特征的影响. 结果表明:自适应网络中的重连规则可以有效减缓病毒传播速度,降低病毒传播规模;随机重连规则使得网络统计特征趋于随机网络;基于元胞自动机建立的传播模型清晰地表达了病毒在传播过程中的双稳态现象. 关键词： 自适应网络 传播动力学 网络动力学 元胞自动机     

新的具有光滑二次函数混沌系统的构建与实现

拓展和改变Lorenz混沌系统的非线性函数,构建一个新的具有光滑二次函数的自治混沌系统,系统包含3个系统变量乘积的非线性函数项和5个平衡点,详细讨论了平衡点的性质并计算了分形维数.利用分岔图和Lyapunov指数谱对系统随参数变化的情况进行分析后得出,系统会发生倍周期分岔.用数字信号处理芯片对混沌系统进行硬件实现,实验结果表明理论分析的正确性以及系统具有较为复杂的动力学行为. 关键词： 混沌系统 分岔图 Lyapunov指数 数字信号处理     

横向补给系统高架索的稳定性与分岔研究

考虑集中质量对系统动力学行为的影响,建立了横向补给系统高架索振动的理论模型.利用Galerkin方法和多尺度方法对动力学方程进行渐近分析.通过对系统Jacobi矩阵特征值的讨论,分析了系统的稳定性.根据系统渐近解的消除永年项条件,得到了系统的振幅分岔方程.借助Mathematica软件,对系统的局部分岔行为进行研究,得到了系统的转迁集以及相应的局部分岔图,研究表明横向补给系统高架索的振动中存在的多种分岔现象.     

非线性切换系统的动力学行为分析

建立了周期切换下的非线性电路模型,基于子系统平衡点及其稳定性分析,分别给出了其相应的fold分岔和Hopf分岔条件,讨论了子系统在不同平衡态下由周期切换导致的各种复杂行为,指出切换系统的周期解随参数的变化存在着倍周期分岔和鞍结分岔两种失稳情形,并相应地导致不同的混沌振荡,进而结合系统轨迹及其相应的分岔分析,揭示了各种振荡模式的动力学机理. 关键词： 周期切换 倍周期分岔 鞍结分岔 混沌     

基于Washout滤波器的Rössler系统Hopf分岔控制

针对Rössler系统平衡点的Hopf分岔,以Washout滤波器为控制器,详细讨论了控制器参数对Hopf分岔点位置、分岔类型以及周期解振幅的控制问题.首先根据Routh-Hurwitz判据计算了受控系统的参数空间稳定域,找出了对应的Hopf分岔边界,并由此分析了滤波器时间常数、线性控制增益对分岔点位置的影响.然后,引入Normal Form直接法方便地求出系统Hopf分岔Normal Form系数,由此确定出改变分岔类型和周期解振幅的控制器非线性增益选择原则.最后用数值计算验证了本文的结论. 关键词： Rö ssler系统 Washout滤波器 Hopf分岔 Normal Form     

V2控制Buck变换器分岔与混沌行为的机理及镇定

V²控制的Buck变换器在反馈放大系数变化的情况下表现出丰富的非线性行为. 本文建立了V²控制Buck变换器的离散迭代模型, 利用单值矩阵方法研究了系统不稳定行为. 随着反馈放大系数的增大, 变换器从稳定的周期一状态发生一系列的倍周期分岔现象进入周期二、周期四, 不断倍化直至混沌态. 同时其单值矩阵的最大特征值也沿着实负轴穿越单位圆, 从而从稳定性的角度揭示了系统发生一系列倍周期分岔的机理. 基于单值矩阵理论, 利用正弦电压补偿方法镇定了系统的分岔和混沌行为, 得到了镇定后系统的稳定边界. 仿真和实验结果证明了本文分析方法和结论的正确性. 关键词： V²控制')" href="#">V²控制 Buck变换器 分岔 镇定控制     

具有多分界面的非线性电路中的非光滑分岔

本文分析了具有多分界面的非线性电路在不同时间尺度下的快慢动力学行为. 在一定的参数条件下,系统的周期解为簇发解,表现出明显的快慢效应. 根据状态变量变化的快慢,把全系统划分为快子系统和慢子系统两组. 根据快慢分析法将慢变量看作快子系统的控制参数,分析了快子系统的平衡点在向量场不同区域内的稳定性. 非光滑系统的分岔与向量场的分界面密切相关,对于具有快慢效应的两时间尺度非光滑系统,快子系统的分岔则取决于分界面两侧平衡点的性质. 通过在临界面引入广义Jacobi矩阵,讨论了快子系统非光滑分岔的类型,即多次穿越分 关键词： 非线性电路 多分界面 非光滑分岔 快慢效应     

Analysis of epidemic models with demographics in metapopulation networks

In this paper, two susceptible–infected–susceptible (SIS) epidemic models are presented and analyzed by reaction–diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.     

Global dynamics of a novel multi-group model for computer worms

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.     

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number R0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if R0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If R0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of R0, when the stochastic system obeys some conditions and R0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable.Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.     

Stability of SIRS system with random perturbations

Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is an SIRS model with or without distributed time delay influenced by random perturbations. We present the stability conditions of the disease-free equilibrium of the associated stochastic SIRS system.     

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.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

Internal symmetry groups of quantum geons

In canonical quantum gravity asymptotically trivial diffeomorphisms not deformable to the identity can act nontrivially on the quantum state space. We show that for many 3-manifolds, the inequivalent diffeomorphisms comprise coverings in SU(2) of crystallographic groups. When the diffeomorphism R_2π associated with 2π-rotation is nontrivial, state vectors can have half-integral angular momentum; we list all 3-manifolds with R_2π trivial.     

Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12:Cr3+ and Their Pressure-Induced Shifts

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), at 300 K, the `pure electronic' contributions and the contributions from EPI to R₁ line, R₂ line, and U band of GGG:Cr³⁺ as well as their PS have been calculated, respectively. The total calculated results are in good agreement with all the experimental data. Their physical origins have been explained. It is found that the mixing-degree of |t₂²(³T₁)e ⁴T₂> and |t₂³²E> base-wavefunctions in the wavefunctions of R₁ level of GGG:Cr³⁺ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role for PS of R₁ line or R₂ line. At 300 K, both the temperature-independent contribution to R₁ line (or R₂ line or U band) from EPI and the temperature-dependent one are important. The remarkable difference between pressure-dependent behaviors of PS of R₁ lines of GGG:Cr³⁺ and GSGG:Cr³⁺ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr³⁺ at various pressures have satisfactorily been explained.     

Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R'₃, R'₂, and R'₁ lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R₁ line and R₂ line of YAG:Cr³⁺ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr³⁺ ion in YAG:Cr³⁺ is compressed along the [111] direction. Thus, for YAG:Cr³⁺ and ruby, the splitting of t₂³⁴A₂ (or t₂³²E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R₁ and R₂ lines of YAG:Cr³⁺, the temperature-dependent contributions due to EPI are dominant.