三维捕食链周期非自治扩散系统正w周期解的存在性

对三种群非自治捕食链扩散系统的持续性生存进行了进一步的讨论。继之 ,又对周期的该系统进行了分析 ,得到了该系统存在唯一的严格正的全局渐近稳定的 w周期解的条件     

拟线性系统的脉冲控制器及其稳定鲁棒性研究

通过分析拟线性系统的稳定性，得到了一类拟线性脉冲控制系统渐近稳定的一个充分条件，由此为这类系统设计了脉冲控制器，解决了这类线性系统的镇定问题，进一步分析了这类拟线性脉冲系统的鲁棒性。     

强稳定的线性两步公式

本文研究一阶常微分方程数值解的收敛性与稳定性,利用最优化方法,确定最优系数,得到三个强稳定的线性两步公式.经过实际计算,结果优于目前的线性两步公式.     

电场中不均匀导电媒质的电荷分布及其应用

利用高斯定理和电荷守恒原理,求得电场中不均匀导电媒质的电荷分布规律,发现电荷分布与电场强度大小和方向及媒质的不均匀性有关,与初始条件无关,而且稳定电场和似稳电场中电荷分布是相同的。应用所得理论结果,对裸眼井井壁的面电荷分布和地层冲洗带内的体电荷分布情况作了初步的探讨。     

具无穷可分分布的稳定线性过程

本文研究系统噪声服从无穷可分分布的稳定线性过程，在简单的条件下，证明了该过程的边沿分布是无穷可分的，并给出边沿分布函数的解析表达式．     

发展方程Ut=aup的恒稳定的差分格式

对发展方程u_t=au_p(a是常数,u_p=■~pu/■x~p,P=1,2,…)引入稳定项,构造了一组新的带参数、相容且恒稳定的三层差分格式.其中P为偶数的格式(2.6)是显格式,是Du Fort—F■ankel格式的推广;P为奇数的格式(3.2),(3.3)及(3.4)是半显格式,可显式计算,(3.5)与(3.6)是隐格式,它们对应的线性方程组的系数矩阵为三对角线阵,可用追赶法求解.     

STABILIZATION OF A KIND OF PREY-PREDATOR MODEL WITH HOLLING FUNCTIONAL RESPONSE

The stabilization problem of a kind of prey-predator model with Holling functional responseis investigated.By approximate linearization approach,a feedback control law stabilizing the closed-loop system is obtained.On the other hand.by exact linearization approach,a suitable change ofcoordinates in the state space and a feedback control law render the complex nonlinear system to bea linear controllable one such that the positive equilibrium point of the closed-loop system is globallyasymptotically stable.     

SOME PROBLEMS OF LYAPUNOV METHOD IN LINEAR CONTINUOUS-TIME SYSTEM

In this paper,some problems of Lyapunov method in linear continuous-time systemare discussed.In part 1,some motivations are given.In part 2,in order to get a good estimate ofthe decaying time in the system,the concept of appropriate Lyapunov function is introduced andthe condition of the system is given to guarantee the existence of the appropriate Lyapunov functionAn application of the appropriate Lyapunov function is introduced to give the bound of time varyingperturbation for the stable system.In part 3,some extensions of the Lyapunov asymptotical stabilitytheorem are given,where the condition of the total derivative of the Lyapunov function along thetrajectory of the system can be reduced from negative definiteness to semi-negative definiteness andcommon quadratic forms with some reasonable conditions,the example shows the extensions areinteresting.     

随机导数的等价定义

讨论了随机导数，并给出和证明了随机可导的等价条件ＺＱＭ和