退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS

1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f…     

含两时滞捕食-被捕食系统的稳定性及分歧

本文研究一类含两相异时滞的捕食－被捕食系统的稳定性及分歧。首先，我们讨论两相异时滞对系统唯一正平衡点的稳定性的影响，通过对系数与时滞有关的特征方程的分析，建立了一种稳定性判别性。其次，将一个时滞看成分歧参数，而另一个看作固定参数，我们证明了该系统具有HOPF分歧特性。最后，我们讨论了分歧解的稳定性。     

OSCILLATION OF DIFFERENTIAL EQUATION ON CYLINDRICAL SURFACE

1IntroductionWhenthebehaviorofdynamicalautonomoussysterllislrlapedontothephasespace,weaskthatabeha,viorofsystemafldapointofthephasespa(fetobemutualone-to-Onecontinuouscorrespondence.FOrthenon-autonomoussystemweaskthatabehaviorofsystemtocorrespondwithonlyo…     

Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

We investigate a system of two nonlinear age-structured partial differential equations describing the dynamics of proliferating and quiescent hematopoietic stem cell (HSC) populations. The method of characteristics reduces the age-structured model to a system of coupled delay differential and renewal difference equations with continuous time and distributed delay. By constructing a Lyapunov–Krasovskii functional, we give a necessary and sufficient condition for the global asymptotic stability of the trivial steady state, which describes the population dying out. We also give sufficient conditions for the existence of unbounded solutions, which describe the uncontrolled proliferation of HSC population. This study may be helpful in understanding the behavior of hematopoietic cells in some hematological disorders.     

退化时滞差分系统的通解

讨论具有时滞的退化差分系统，给出其初始函数的相容性条件，并给出其通解，最后举例说明之．     

New complexity results on scheduling with small communication delays

Although most of the scheduling problems with interprocessor communication delays have been shown to be NP-complete, some important special cases were still unsolved. This paper deals with the problem where communication times are smaller than processing times and task duplication is not allowed. We prove that this problem is NP-complete and we give an efficient approximate algorithm with performance guarantee.     

中立型比例延迟微分系统线性θ-方法的渐近估计

本文研究了一类线性非自治中立型比例延迟微分系统线性θ-方法的渐近稳定性,并借助于泛函不等式得到了数值解的渐近估计.此渐近估计不仅比数值渐近稳定性描述得更加精确,而且还能给出非稳定情形数值解的上界估计式.数值算例验证了相关理论结果.     

一类具有脉冲预防接种的SEIRS传染病模型的研究

研究了一类具有脉冲预防接种的SEIRS传染病模型,利用对模型等价系统的分析,得到了模型无病周期解具有全局吸引性的存在条件,并且给出了疾病的持久性的存在条件.     

广义的Lotka—Volterra方程的全局渐近稳定性

通过构造李亚普诺夫函数的方法,研究了广义的Lotka—Volterra时滞模型方程,而且给出了正平衡点的全局渐近稳定性的充分必要条件,同时对前人的结果进行了改进和推广．     

Turing-Hopf bifurcation in the reaction-diffusion system with delay and application to a diffusive predator-prey model

The interactions of diffusion-driven Turing instability and delay-induced Hopf bifurcation always give rise to rich spatiotemporal dynamics. In this paper, we first derive the algorithm for the normal forms associated with the Turing-Hopf bifurcation in the reaction-diffusion system with delay, which can be used to investigate the spatiotemporal dynamical classification near the Turing-Hopf bifurcation point in the parameter plane. Then, we consider a diffusive predator-prey model with weak Allee effect and delay. Through investigating the dynamics of the corresponding normal form of Turing-Hopf bifurcation induced by diffusion and delay, the spatiotemporal dynamics near this bifurcation point can be divided into six categories. Especially, stable spatially homogeneous/inhomogeneous periodic solutions and steady states, coexistence of two stable spatially inhomogeneous periodic solutions, coexistence of two stable spaially inhomogeneous steady states and the transition from one kind of spatiotemporal patterns to another are found.     

Global analysis of a delayed epidemic dynamical system with pulse vaccination and nonlinear incidence rate

This study explores the influence of epidemics by numerical simulations and analytical techniques. Pulse vaccination is an effective strategy for the treatment of epidemics. Usually, an infectious disease is discovered after the latent period, H1N1 for instance. The vaccinees (susceptible individuals who have started the vaccination process) are different from both susceptible and recovered individuals. So we put forward a SVEIRS epidemic model with two time delays and nonlinear incidence rate, and analyze the dynamical behavior of the model under pulse vaccination. The global attractivity of ‘infection-free’ periodic solution and the existence, uniqueness, permanence of the endemic periodic solution are investigated. We obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. The main feature of this study is to introduce two discrete time delays and impulse into SVEIRS epidemic model and to give pulse vaccination strategies.     

CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS WITH VARIABLE DELAY

Ｃｏｎｓｉｄｅｒｔｈｅｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈａｖａｒｉａｂｌｅｄｅｌａｙｘｎ－ｘｎ－１＝Ｆ（ｘｎ，ｘｒ（ｎ），ｎ＝ｎ０，ｎ０＋１，…（１）ｗｈｅｒｅ（Ｈ１）：Ｆ∈Ｃ（Ｒ×Ｒ，Ｒ），Ｆ（ｕ，ｖ）ｉｓｄｅｃｒｅａｓｉｎｇｗｉｔｈｒｅｓ...     

Stability of time-varying switched systems with time-varying delay

In this paper, we investigate the stability of time-varying switched systems with time-varying delay. We first give a generalization of Halanay’s inequality and then use this inequality to obtain sufficient conditions for the stability of switched systems.     

一类退化时滞微分系统解的稳定性

讨论了指标为1的退化时滞微分系统解的稳定性,并给出一个具体的V-泛函和相应的定理.     

非线性无穷时滞微分系统的稳定性

本文主要内容是：（１）在局部条件下，建立了一类具有无穷时滞的非线性的正、反向积分微分不等式；（２）结合常数变易法和Ｌｉａｐｕｎｏｖ函数法（不必寻找Ｐ－函数），利用所建立的不等式研究了非线性无穷时滞微分系统的稳定性；（３）举例说明了本文定理的应用和优点。     

General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays

For a family of differential equations with infinite delay, we give sufficient conditions for the global asymptotic, and global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Cohen-Grossberg type, with both bounded and unbounded distributed delay, for which general asymptotic and exponential stability criteria are derived. As illustrations, the results are applied to several concrete models studied in the literature, and a comparison of results is given.     

Existence-Uniqueness Problems For Infinite Dimensional Stochastic Differential Equations With Delays

The main aim of this paper is to develop the basic theory of a class of infinite dimensional stochastic differential equations with delays (IDSDEs) under local Lipschitz conditions. Firstly, we establish a global existence-uniqueness theorem for the IDSDEs under the global Lipschitz condition in \(C\) without the linear growth condition. Secondly, the non-continuable solution for IDSDEs is given under the local Lipschitz condition in \(C\). Then, the classical Itô's formula is improved and a global existence theorem for IDSDEs is obtained. Our new theorems give better results while conditions imposed are much weaker than some existing results. For example, we need only the local Lipschitz condition in \(C\) but neither the linear growth condition nor the continuous condition on the time \(t\). Finally, two examples are provided to show the effectiveness of the theoretical results.