On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.     

非自治动力系统中逐点跟踪性和极限跟踪的研究

根据离散动力系统中逐点跟踪性和极限跟踪性的定义,引入非自治动力系统中逐点跟踪性和极限跟踪性的概念,研究了非自治动力系统中逐点跟踪性和极限跟踪性的动力学性质,得到如下结果:1)若F={f_i}_i=0^∞拓扑共轭于G={g_i}_i=0^∞,则F具有逐点跟踪性当且仅当G具有逐点跟踪性;2)乘积系统(X×Y,F×G)具有逐点跟踪性当且仅当(X,F)和(Y,G)具有逐点跟踪性;3)乘积系统(X×Y,F×G)具有极限跟踪性当且仅当(X,F)和(Y,G)具有极限跟踪性.这些结果丰富了非自治动力系统中逐点跟踪性和极限跟踪性的理论.     

On the uniform hyperbolicity of some nonuniformly hyperbolic systems

We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability (probability one with respect to every invariant probability measure) are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.

     

一类不连续非自治系统的一致最终有界性

主要讨论右端不连续的非自治系统在Filippov解意义下的一致最终有界性问题.首先给出不连续系统全局强一致最终有界的定义,并得到了不连续系统全局一致强最终有界的Lya- punov定理.最后给出了在一类带有不连续摩擦项的力学系统中的应用.     

On the Instability of Linear Nonautonomous Delay Systems

The unstable properties of the linear nonautonomous delay system x(t) = A(t)x(t) + B(t)x(t – r(t)), with nonconstant delay r(t), are studied. It is assumed that the linear system y(t) = (A(t) + B(t))y(t) is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay r(t) is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function r(t) and the results depending on the asymptotic properties of the delay function.     

集值离散系统的某些动力性质

A discrete dynamical system can be expressed as xn 1 =f(xn), n=0,1, 2,... where X isa metric space and f : X→X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]).     

高维非自治系统的周期解

本文利用指数型二分性理论和不动点方法考虑系统Ｘ＝ｆ（ｔ,ｘ）,Ｘ＝Ａ（ｔ,ｘ）ｘ＋ｂ（ｔ,ｘ）的周期解的存在性问题,其中Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵函数,ｆ（ｔ,ｘ）,ｂ（ｔ,ｘ）是ｎ维连续向量函数,且关于ｔ以ｗ＞０为周期,所得结果推广了王联和曾唯尧的结果．     

On the Dynamics of Nonautonomous General Dynamical Systems and Differential Inclusions

This paper is concerned with the dynamics of nonautonomous general dynamical systems (NAGDSs in short) and applications to differential inclusions on ? ^m . First, we show that if a NAGDS has a compact uniformly attracting set, then it has a pullback attractor $\mathcal{A}$ with the parametrically inflated pullback attractor $\mathcal{A}(\varepsilon_0)$ being uniformly forward attracting. Then, we establish some stability results for pullback attractors. Finally, we apply the abstract theory to nonautonomous differential inclusions on ? ^m to obtain some interesting results. In particular, the effects of small time delays to asymptotic stability is addressed.     

具有时滞的非自治Lotka-Volterra竞争系统的持久与灭绝

本文研究具有纯时滞的一般Ｎ－种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的持久性和灭绝性．一些新的判别准则被建立．文献［８－１０］中得到的关于无时滞非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的结果被改进和推广．     

Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems

The article is devoted to the study of the relation between forward and pullback attractors of set-valued nonautonomous dynamical systems (cocycles). Here it is proved that every compact global forward attractor is also a pullback attractor of the set-valued nonautonomous dynamical system. The inverse statement, generally speaking, is not true, but we prove that every global pullback attractor of an α-condensing set-valued cocycle is always a local forward attractor. The obtained general results are applied while studying periodic and homogeneous systems. We give also a new criterion of the absolute asymptotic stability of nonstationary discrete linear inclusions. Dedicated to our friend Professor Enrico Primo Tomasini on the occasion of his 55th birthdayMathematics Subject Classifications (2000) Primary: 34C35, 34D20, 34D40, 34D45, 58F10,58F12, 58F39; secondary: 35B35, 35B40.     

具有时滞的非自治Lotka-Volterra竞争系统的持久与灭绝

本文研究具有纯时滞的一般Ｎ－种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的持久性和灭绝性．一些新的判别准则被建立．文献［８－１０］中得到的关于无时滞非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统的结果被改进和推广．     

Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays

By using the continuation theorem of coincidence degree theory,the sufficient conditions to guar-antee the existence of positive periodic solutions are established for nonautonomous predator-prey systems withdiscrete and continuously distributed delays.     

On Infinite Systems of Linear Autonomous and Nonautonomous Stochastic Equations

The solvability of autonomous and nonautonomous stochastic linear differential equations in is studied. The existence of strong continuous (L^p-continuous) solutions of autonomous linear stochastic differential equations in with continuous (L^p-continuous) right-hand sides is proved. Uniqueness conditions are obtained. We give examples showing that both deterministic and stochastic linear nonautonomous differential equations with the same operator in may fail to have a solution. We also establish existence and uniqueness conditions for nonautonomous equations.     

On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems

The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable;every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points; and a set-valued dynamical system admits an eventually shadowable point if and only...     

脉冲微分方程的两度量实用稳定性

利用向量Lyapunov函数,研究了脉冲微分方程的两度量实用稳定性问题,通过实例对得到的稳定性的结论给予了验证.     

关于Banach空间中一类非线性方程的若干问题

本文引入边界条件（Ｓｗ，Ａ，ａ）与（ＬＭ，ｗ），建立有关ｋ－集压缩局部固有场的延拓与不动点指数计算的一些结果；结合弱半可微性，研究一类非线性方程的正解、多正解和固有元集等问题，作为一个应用，还研究了两点边值问题。     

On the Theory of Optimal Processes in Discrete Systems

Mathematical Notes - In this paper, by introducing the notion of γ-convex set, we distinguish a wider class of discrete control systems in which the global maximum principle holds. A new type...     

Banach空间中增生算子T的方程f=x＋Tx的迭代解

在具有一致凸对偶空间的Banach空间中讨论了关于增生算子T的方程f=x Tx的迭代解,其结果推广和改进了Chidume和Zhu的结果。