两类网络蠕虫的模型建立及动力学性态分析

网络蠕虫之间存在着复杂的关系,它们对蠕虫的传播和演化等动力学行为有着重要的影响,刻画这些关系有助于找到更好的控制和预防策略.本文建立了两类蠕虫(蠕虫I、蠕虫II)传播的数学模型,通过分析得到两个阈值条件R_1和R_2,当R_11和R_21,无病平衡点全局渐近稳定,意味着两类蠕虫最终均被清除;当R_21R1边界平衡点Q_1全局渐近稳定,也即蠕虫II灭绝,蠕虫I将持续存在;当R_11R2边界平衡点Q2全局渐近稳定,也即蠕虫I灭绝,蠕虫II将持续存在;当R_11和R21时,存在惟一正平衡点且全局渐近稳定,即两类蠕虫(蠕虫I与蠕虫II)同时持续存在.通过理论分析可以得到要控制蠕虫病毒可以通过控制参数来实现,进一步给出控制蠕虫病毒相对应的措施.最后通过数值模拟验证了理论分析结果.     

一种具有脉冲扰动的恒化器模型的动力学性质

在这篇文章中,我们提出并分析了一个具有捕食者,食饵和既有周期脉冲输入又有周期脉冲输出营养液的恒化器模型.我们得到了一种微生物和营养液共存的周期解,同时,也得到两种微生物都绝灭的周期解,而且建立了周期解稳定的充分条件.最后,我们给出了一个简单的讨论.     

Dynamical Behaviors of a Stochastic Single-Species Model with Allee Effects

Methodology and Computing in Applied Probability - In this letter, we test a scalar stochastic nonlinear equation used to portray the growth of a population with Allee effects. We first testify...     

Dynamical Behaviors in a Two-dimensional Map

We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto‘s theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.     

Dynamics of certain class of critically bounded entire transcendental functions

Let E denote the class of all transcendental entire functions for z∈C and an?0 for all n?0 such that f(x)>0 for x<0 and the set of all (finite) singular values of f forms a bounded subset of R. For each f∈E, one parameter family is considered. In this paper, we mainly study the dynamics of functions in the one parameter family S. If f(0)≠0, we show that there exists a positive real number λ^∗ (depending on f) such that the bifurcation and the chaotic burst occur in the dynamics of functions in the one parameter family S at the parameter value λ=λ^∗. If f(0)=0, it is proved that the Julia set of fλ is equal to the complement of the basin of attraction of the super attracting fixed point 0 for all λ>0. It is also shown that the Fatou set F(fλ) of fλ is connected whenever it is an attracting basin and the immediate basin contains all the finite singular values of fλ. Finally, a number of interesting examples of entire transcendental functions from the class E are discussed.     

具有暂时免疫传染病模型同宿分支

讨论了具有暂时免疫传染病模型同宿轨道分支的存在性,利用Melnikov函数确定了系统双曲不动点的稳定和不稳定流形的相对位置,从而给出存在极限环的参数范围.     

Dynamical behavior of an epidemic model with a nonlinear incidence rate

In this paper, we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action. By carrying out global qualitative and bifurcation analyses, it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region. When such a region exists, it is shown that the model undergoes a Bogdanov-Takens bifurcation, i.e., it exhibits a saddle-node bifurcation, Hopf bifurcations, and a homoclinic bifurcation. Existence of none, one or two limit cycles is also discussed.     

Dynamical behaviors of a prey-predator system with impulsive control

In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis.     

A Characterization of Topologically Transitive Attributes for a Class of Dynamical Systems

In this work,by virtue of the properties of weakly almost periodic points of a dynamical system (X,T) with at least two points,the authors prove that,if the measure center M(T) of T is the whole space,...     

The Stage-structured Predator-Prey System with Delay and Harvesting

In this article, we establish a mathematical model of two species with stage structure and the relation of predator-prey, obtain the necessary and sufficient condition for the permanence of two species and the extinction of one species or two species. We also obtain the optimal harvesting and the threshold of harvesting for the sustainable development and increasing delays can cause a bifurcation into periodic solutions. Finally, we give some numerical results and graphs.     

A Finite-Dimensional Dynamical Model for Gelation in Coagulation Processes

Summary. We study a finite-dimensional system of ordinary differential equations derived from Smoluchowski's coagulation equations and whose solutions mimic the behaviour of the nondensity-conserving (geling) solutions in those equations. The analytic and numerical studies of the finite-dimensional system reveals an interesting dynamic behaviour in several respects: Firstly, it suggests that some special geling solutions to Smoluchowski's equations discovered by Leyvraz can have an important dynamic role in gelation studies, and, secondly, the dynamics is interesting in its own right with an attractor possessing an unexpected structure of equilibria and connecting orbits. Received April 26, 1997; revised October 3, 1997; accepted October 23, 1997     

Morgan-Mercer-Flodin模型和Weibull模型的拟合

Morgan-Mercer-Flodin模型和 Weibull模型是两个著名的四参数 S形生长模型 .在一定的正则变换下 ,它们的隐函数方程及未线性化参数与拐点特征之间的联系都非常相似 .从而可用完全相同的方法对它们的未线性化参数初始值进行搜索 ,以拟合隐函数曲线的 GNL法对它们进行最小二乘拟合 .还用实例对这种算法进行了验证 .     

Chaotic behavior analysis based on corner bifurcations

In this paper, a mathematical analysis in order to generate a chaotic behavior for bounded piecewise smooth systems of dimension three submitted to one of its specific bifurcations, namely the corner one, is proposed. This study is based on period doubling method.     

种群生态系统中的模糊软测量方法

经典的生物模型中,关键参数的难以测量使整个动力系统具有较大的不确定性.本文引入模糊软测量技术,以湿地环境中三种群生态系统为例,将软洲量技术与模糊系统结合应用于种群动力学模型,以种群数量的初始值、时间t及种群变化率为辅助参数进行种群数量的预测.运用软测量技术估计微分方程中关键参数(如竞争系数、最大捕获率、能量转换系数),建立确定的动力学微分方程模型.仿真结果显示此方法的可行性、有效性.     

二维水动力弥散的随机数学模型

首先以二维水动力弥散实验为基础 ,根据实验所提供的信息 ,建立了二维水动力弥散实验的随机水质数学模型 .其次我们对所建模型进行了数值模拟计算 ,计算结果与实测数据比较吻合 ,从而说明所建立的随机模型是合理的 ,有实际应用价值 .     

长水波近似方程组的动力学行为和辛几何算法

长水波近似方程组作为一类重要的非线性方程有着许多广泛的应用前景,特别是在浅水非线性色散波的研究中具有重要意义.给出了长水波近似方程组的动力学行为,并基于Hamilton空间体系的多辛理论研究了长水波近似方程组的数值解法,讨论了利用Preissmann方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,格式满足多辛守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性.     

Model companion and model completion of theories of rings

Extending the language of rings to include predicates for Jacobson radical relations, we show that the theory of regular rings defined by Carson, Lipshitz and Saracino is the model completion of the theory of semisimple rings. Removing the requirement on the Jacobson radical (reduced to {0}), we prove that the theory of rings with no nilpotents does not admit a model companion relative to this augmented language.      

一类时滞离散动力系统及其截断系统定性行为的研究

研究了一类时滞离散动力系统的一次截断系统,仔细分析其分支行为和混沌性态等定性行为.与原系统进行比较,证明二者主要的定性行为非常相似.最后对未来工作提出几点建议.     

一个具有非线性接触率和种群动力学的传染病模型

本文研究了具有非线性接触率和易感类中具有Ｌｏｇｉｓｔｉｃ增长的ＳＩ传染病模型的正不变集，平衡位置以及平衡位置的稳定性。