非线性系统有理首次积分的不存在性和部分存在性

该文的目的是给出一般非线性系统存在和部分存在有理首次积分的判别准则. 作者给出系统存在有理首次积分的必要条件, 在此基础上进一步给出系统不存在其它有理首次积分(在函数独立的意义下)的判定准则.     

周期扰动下卫星运动系统的动力学性质

本文运用Melnikov方法对平面卫星运动系统在周期扰动下所表现出来的动力学性质进行了探讨.首先运用次谐Melnikov方法给出了卫星轨道在周期扰动下存在次谐周期轨道的条件,并进一步运用同宿.Melnikov方法证实了该系统存在Smale马蹄意义下的混沌性质.     

具有多重严重故障和非严重故障和修复功能的系统的可靠性分析

该文研究一个具有多重严重故障和非严重故障和修复功能的系统的可靠性问题. 在泛函分析理论的框架下,将系统方程组写成一个 Banach 空间中的抽象初值问题,利用算子半群方法,研究了该系统的适定性、稳态解的存在性以及稳定性.表明: 在系统模型的假定下,所研究的系统是适定的,存在非负动态解和稳态解, 特别在范数意义下动态解收敛到稳态解.从而由系统稳态解得到的系统指标是可靠的.     

具有趋化性的非线性系统的解的爆破性态分析

讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.     

一个可逆马氏过程的协方差与长程相关性分析(英文)

本文对一个存在聚合与断裂反应的马氏过程进行了研究,分析了三种状态(下临界状态、临界状态、上临界状态)下系统中的不同大小的分子之间的协方差,并证明了只有在临界状态下系统中存在长程相关性.     

R~2中具有趋化性的抛物-椭圆系统的解的性态分析

在二维空间中讨论了一个抛物-椭圆系统,而该系统来源于生物学中的趋化性模型.主要在Sobolev空间的框架下讨论了解的全局存在性与解的爆破性质,得出结论该系统存在一个门槛值,而该值决定了解全局存在或者发生爆破.最后利用利李亚普诺夫函数给出了定理的证明并得出结论.     

测度中心为单点集的强拓扑混合系统

本文用构造性的方法证明了存在强拓扑混合的紧致系统,其测度中心是单点集.从而说明了拓扑混合的系统在拓扑的观点下是复杂的,但在遍历的意义下却可能是简单的.     

广义双色散热耦合方程组的初边值问题

研究了一类广义双色散热耦合方程组的初边值问题在齐次边界条件下的吸引子.首先通过Faedo-Galerkin方法证明了整体解的存在唯一性;其次通过证明系统的衰减性和渐近紧性,得到了系统存在全局吸引子;最后证明了该系统的全局吸引子存在有限分形维数.     

具有热储备的可修复平行系统在由常规错误引起失效下的渐进稳定性

讨论了具有热储备和两个独立相同部件的平行系统在由常规错误引起失效下的渐进稳定性.首先,利用Banach空间的Volttera算子方程得到了非负动态解的存在唯一性;然后,利用强连续线性算子半群理论证明了系统正的动态解的存在唯一性,而由于初始值不在定义域内,故得到的是mild解.但在t＞0时系统古典解存在唯一,所以此时mild解即为古典解.最后,利用线性算子半群稳定性的结果,证明了该动态解在范数意义下收敛到稳态解,进而得到了系统的渐进稳定性.     

状态反馈脉冲控制比率依赖Holling-Tanner系统的周期解

本文研究具有状态反馈脉冲控制的比率依赖Holling-Tanner系统.在连续系统的正平衡点为不稳定焦点的前提下,利用微分方程几何理论及后继函数方法,获得脉冲系统阶1周期解的存在性、唯一性及轨道稳定性.利用数值模拟验证主要结论,并且数值结果得到在极限环内脉冲系统存在阶k周期解.最后,给出主要结论.     

Characterizations of the Optimal Descartes' Rules of Signs

A system of functions satisfies Descartes' rule of signs if the number of zeros (with multiplicities) of a linear combination of these functions is less than or equal to the number of variations of strict sign in the sequence of the coefficients. In this paper we characterize the systems of functions satisfying a stronger property than the above mentioned Descartes' rule: The difference between the number of zeros and the changes of sign in the sequence of coefficients must be always a nonnegative even number. We show that the approximation to the number of zeros given by these systems of functions is better than the approximation provided by any other systems of functions satisfying a Descartes' rule of signs. This last result improves, in the particular case of polynomials, the main theorem of [14].     

Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory

A class of second-order abstract systems with memory and Dirichlet boundary conditions is investigated. By suitable Liapunov functionals, existence of solutions as well as asymptotic behavior, are determined. In particular, when the memory kernel decays exponentially, the polynomially decay of the solutions is proved.     

Real-time calculation of the current state estimates for a class of delay systems

The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.     

A variable dimension fixed point algorithm and the orientation of simplices

A variable dimension algorithm with integer labelling is proposed for solving systems ofn equations inn variables. The algorithm is an integer labelling version of the 2-ray algorithm proposed by the author. The orientation of lower dimensional simplices is studied and is shown to be preserved along a sequence of adjacent simplices.     

On the Convergence of Formal Solutions of a System of Partial Differential Equations

We study a version of the classical problem on the convergence of formal solutions of systems of partial differential equations. A necessary and sufficient condition for the convergence of a given formal solution (found by any method) is proved. This convergence criterion applies to systems of partial differential equations (possibly, nonlinear) solved for the highest-order derivatives or, which is most important, “almost solved for the highest-order derivatives.”     

在连续的时间系统中不存在Shilnikov型混沌

在n维的、时间连续的光滑系统中,得到了不存在同宿轨道和异宿轨道的条件.基于此结论并用一个基本实例,推断出如下结论:在多项式常微分方程系统中,有着以不存在同宿轨道和异宿轨道为特征的第4类混沌.     

Numerical method of lines for parabolic functional differential equations

Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the numerical method of lines are given. An explicit Euler method is proposed for the numerical solution of systems thus obtained. This leads to difference scheme for the original problem. A complete convergence analysis for the method is given.     

Oscillation Theorem of Systems of Quasilinear Impulsive Delay Hyperbolic Equations

In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.     

拟线性脉冲时滞双曲型方程组的振动性定理

In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.