基于两类媒介的炭疽传播模型的全局动力学分析

为了研究动物种群中媒介对炭疽传播的影响,该文依据尸食性蝇与血食性蝇的传播机制,建立了一个确定性传染病模型.利用微分方程基本定理证明了模型解的非负性和有界性,给出了平衡点存在的充分条件,定义了模型的几类再生数,利用线性化方法和M-矩阵等方法对平衡点的稳定性进行了分析,并研究了疾病的持久性.利用数值模拟研究了参数对基本再生数的影响.研究结果表明:及时清理染病尸体,尽量消除苍蝇的繁殖地点,对苍蝇使用杀虫剂对炭疽在动物种群中传播具有一定的抑制作用.     

G-期望下路径依赖的动态规划原理及相应的偏微分方程

本文研究了G-期望下依赖于右连左极路径的倒向随机微分方程和相应的偏微分方程,给出了依赖于右连左极路径的完全非线性偏微分方程黏性解的定义,证明了相应的动态规划原理,并进一步证明了动态规划原理的值函数为相应的Hamilton-Jacobi-Bellman(HJB)方程的黏性解.     

一类含扩散项的Nicholson苍蝇模型解的渐近行为及其Hopf分支

本文研究了一类含扩散项的Nicholson苍蝇模型在Neumann边值条件下解的渐近行为和Hopf分支,得到了其正解收敛于不同平衡点的充分条件和由平衡点分支出Hopf分支的充分条件.     

两类破碎群体平衡方程接受的李群及群不变解

针对难找到破碎群体平衡方程的精确解和解析方法缺乏的问题,研究两类积分-偏微分方程(破碎群体平衡方程)接受的李群、群不变解、约化积分-常微分方程及精确解.首先采用伸缩变换李群分析方法探寻积分-偏微分方程接受的李群.其次将积分-偏微分方程转化为纯偏微分方程,运用经典李群分析方法计算纯偏微分方程接受的李群.然后利用改进了的李群分析方法结合伸缩变换群和经典李群分析方法获得的结果确定积分-偏微分方程接受的李群.最后找到了积分-偏微分方程接受的李群,给出了积分-偏微分方程的约化积分-常微分方程、群不变解及显式精确解,分析了部分解的动力学行为性质及特征.     

非线性中立型变延迟微分方程的长时间稳定性

该文主要分析非线性中立型变延迟微分方程(NDDEs)的长时间行为,获得了非线性变延迟系统解的一致最终有界性的主要结果.基于此主要结果,得到了非线性中立型延迟微分方程的两个典型特例,常延迟微分方程和比例延迟微分方程,解一致最终有界的充分条件.文章最后给出了一些具体实例以说明这些结果的应用.     

拟线性化方法和微分方程多点边值问题

§1 引言 微分方程数值计算的拟线性化方法,Bellman和Kalaba用于动态规划,McGill和Kenneth、Roberts和Shipman又用于解二阶非线性微分方程的两点边值问题,并给出了算法及其理论基础。文[4]将后者问题作了推广。本文将拟线性化方法用来研究n阶非线性微分方程多点边值问题:     

伊藤-泊松型随机微分方程的线性二次控制

本文研究伊藤-泊松型随机微分方程的线性二次控制问题,利用动态规划方法、伊藤公式等技巧,通过解HJB方程,我们得到了随机Riccati方程及另外两个微分方程,求出控制变量,解决了线性二次最优控制最优问题.     

关于M/M/1动态排队系统解的半稳定性

本文讨论了两类 M/M/1 动态系统的数学模型 ,利用常微分方程所描述的 M/M/1 系统的结果证明了较复杂的偏微分方程所描述的 M/M/1 系统的一些性质 ,该方法简化了已有结果     

小裁缝和巨人

正夏天的一个早晨,小裁缝正在吃早餐。这时,果酱香甜的气味招来了一群聚在墙上的苍蝇。"不许抢我的果酱!"小裁缝赶着苍蝇,可是苍蝇还是越聚越多。小裁缝随手抓起一条毛巾,朝着苍蝇狠命地打了下去,一下子打死了七只苍蝇。"哦,勇敢的小裁缝,你可真了不起!"他说道,全世界的人都应该知道你的壮举。"说罢,小裁缝     

一类非线性中立型微分方程解的振动性

本文研究一类具有分布时滞的三阶非线性泛函微分方程解的振动行为,利用推广的黎卡提变换,通过积分平均方法,获得了泛函微分方程一些新的振动性判据,推广和改进了最近文献中的一些结果.     

On the pursuit problem for linear differential games with distinct constraints on the players’ controls

Pontryagin’s first and second (direct) methods and the so-called third pursuit method are the basic methods of the theory of differential games. We present various modifications of these methods. We analyze linear differential pursuit games for a delay equation under distinct constraints on the players’ control parameters. We give sufficient conditions for the solvability of the pursuit problem in finite time.     

Adaptive greedy approximations

The problem of optimally approximating a function with a linear expansion over a redundant dictionary of waveforms is NP-hard. The greedy matching pursuit algorithm and its orthogonalized variant produce suboptimal function expansions by iteratively choosing dictionary waveforms that best match the function’s structures. A matching pursuit provides a means of quickly computing compact, adaptive function approximations. Numerical experiments show that the approximation errors from matching pursuits initially decrease rapidly, but the asymptotic decay rate of the errors is slow. We explain this behavior by showing that matching pursuits are chaotic, ergodic maps. The statistical properties of the approximation errors of a pursuit can be obtained from the invariant measure of the pursuit. We characterize these measures using group symmetries of dictionaries and by constructing a stochastic differential equation model. We derive a notion of the coherence of a signal with respect to a dictionary from our characterization of the approximation errors of a pursuit. The dictionary elements slected during the initial iterations of a pursuit correspond to a function’s coherent structures. The tail of the expansion, on the other hand, corresponds to a noise which is characterized by the invariant measure of the pursuit map. When using a suitable dictionary, the expansion of a function into its coherent structures yields a compact approximation. We demonstrate a denoising algorithm based on coherent function expansions.     

Position of Principal component analysis among Auto-associative composite models

We introduce Auto-associative composite models, which have shown a good behavior on real data sets, and share important theoretical approximation properties. Their basic principle is to approximate iteratively data by manifolds of increasing dimension. We exhibit a special class of such models: auto-associative additive models. Their use is widespread in Projection pursuit regression. First, we show that Principal component analysis is a linear auto-associative additive model. Then, we show that principal component analysis is the only auto-associative composite model which is additive.     

Functional-Differential Games with Nonatomic Difference Operator

Ukrainian Mathematical Journal - We study a differential pursuit game in a system dynamically described by a linear functional differential equation. The coefficients of the equation are closed...     

Pursuit problems in linear differential games with delay

In this paper we study linear differential games described by a systemof linear differential equations with delay subject to certain geometric constraints on the control parameters of the players. We obtain sufficient conditions for terminating the pursuit in a finite time.     

On a Multiperson Pursuit Problem with Integral Constraints on the Controls of the Players

We consider a linear multiperson differential game with integral constraints on the control of the players. The pursuit is assumed terminated if the solution of at least one of the equations describing the game reaches the origin at some instant of time.In the case of one pursuer, we obtain a necessary and sufficient condition for terminating pursuit from all points of space. In the case of many pursuers, we obtain a sufficient condition for terminating pursuit from all points of space.     

Existence of value in pursuit-evasion games with restricted phase coordinates

Almost all results referring to the problem of the existence of a value in differential games concern games without restricted phase coordinates. In this paper, we introduce a concept of value for differential games of pursuit and evasion and prove, under some general assumption, the existence of it. The players are required to satisfy some general phase constraints. The arguments employed in this paper are based on some extent on Krasovskii's method of extremal construction. We also show that the lower value in the Friedman sense is a generalization of our value. In a special linear case, the equivalence between pursuit differential games and time-optimal control problems is established.     

Concentrating solutions of some singularly perturbed elliptic equations

We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.      

Asymptotic behaviors of stochastic epidemic models with jump-diffusion

In this paper, we classify the asymptotic behavior for a class of stochastic SIR epidemic models represented by stochastic differential systems where the Brownian motions and Lévy jumps perturb to the linear terms of each equation. We construct a threshold value between permanence and extinction and develop the ergodicity of the underlying system. It is shown that the transition probabilities converge in total variation norm to the invariant measure. Our results can be considered as a significant contribution in studying the long term behavior of stochastic differential models because there are no restrictions imposed to the parameters of models. Techniques used in proving results of this paper are new and suitable to deal with other stochastic models in biology where the noises may perturb to nonlinear terms of equations or with delay equations.     

Linear differential pursuit games with integral constraints in the presence of delay

Problems involving linear differential pursuit games were studied by many authors; their work served as a basis for studying pursuit problems in linear differential games with integral constraints. In the present paper, we obtain sufficient conditions for the solvability of linear pursuit problems with integral constraints on the control of the players in the presence of delay.