非线性非自治系统零解的稳定性及部分稳定性研究

讨论了非线性非自治系统未被扰动运动的全变元及关于部分变元的稳定性、一致稳定性及全局稳定性，给出了几个判定准则，这些定理允许Lyapunov函数的导数为变号函数，改进了已有文献中的有关结果。     

关于扰动微分方程零解稳定性若干定理的改进

本文运用Ляиунов第二方法研究扰动微分方程零解稳定性，分别研讨了所给扰动微分方程的局部稳定性、全局渐近稳定性以及全局一致渐近稳定性问题，得到若干定理，这些结果在一定条件下改进了文[1]的相应结果，运用更加广泛．     

向量参变量的约束集族最大元的通有稳定性

利用集值映射方法定义约束广义最大元,在约束条件和向量参变量意义下,讨论了约束最大元映射、向量参数扰动时,特别是约束条件受到扰动时,向量参变量的约束集族最大元的通有稳定性,在最广的扰动下,获得了通有稳定性定理.     

一类中立型时滞系统周期运动的近似解

对一类中立型时滞系统在临界状态小扰动下的平衡点进行了稳定性分析,同时讨论了该系统在非线性扰动下的周期运动的近似解及稳定性.     

中立型随机比例微分方程的数值解的指数稳定性（英文）

本文主要利用半鞅收敛定理,研究中立型随机比例微分方程的数值稳定性.该文建立了线性的和非线性的中立型随机比例微分方程新的细则,我们将证明,在线性增长条件下,欧拉方法可以保留中立型随机比例微分方程的几乎处处指数稳定性,并且反向的欧拉方法能保留非线性的中立型随机比例微分方程的几乎处处指数稳定性.     

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。     

经过修正的平面Couette流的非线性稳定性研究

本文讨论了经过修正的平面Couette流在二维扰动下的非线性稳定性性质,并同经过修正的平面Poiseuille流的非线性稳定性性质进行了比较.计算结果表明,对于有限振幅的扰动,平面Couette流比平面Poiseulle流更不稳定.     

具时滞扰动的高维系统概周期解的存在性、唯一性和稳定性

本文考虑了一类具时滞扰动的高维系统，利用不动点定理，建立了保证其撬周期解的存在性、唯一性和稳定性的充分性条件，推广了相关文献的主要结论．     

非线性脉冲微分系统的双测度稳定性

该文研究了非线性脉冲微分系统的双测度稳定性问题,借助类似于Ｌｙａｐｕｎｏｖ函数的一类函数,建立了有关双测度稳定性的几个定理,这些定理均不要求类似的Ｌｙａｐｕｎｏｖ函数其广义导数在讨论的整个区域不变号,而只须在一些特殊取值处的导数具有固定的符号,推广和改进了已有的结果．最后阐述了这些定理的应用．     

关于扰动微分方程组零解部分变元的稳定性

本文讨论未被扰动运动关于部分变元的稳定性，一致稳定性和全局渐近稳定性，给出了一种判定，改进了文［１］中的相应定理。     

STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

In this paper,the stability of a class of impulsive functional differential equations with infinite delays is investigated. A uniform stability theorem and a uniform asymptotic stability theorem are established.     

Solution Estimates for Nonlinear Nonautonomous Evolution Equations in Spaces with Normalizing Mappings

Nonlinear nonautonomous evolution equations in a space with a normalizing mapping (a generalized norm) are considered. Solution estimates are established. In particular cases these estimates generalize the Wazewski and Lozinskii estimates from the theory of ordinary differential equations. By the obtained estimates, the following problems are investigated: asymptotic stability, boundedness of solutions, input-output stability, existence of periodic solutions. Applications to integro-differential equations are discussed.     

Coupled coincidence point theorems in ordered metric spaces

In this paper we extend the coupled contraction mapping theorem proved in partially ordered metric spaces by Gnana Bhaskar and Lakshmikantham (Nonlinear Anal. TMA 65:1379–1393, 2006) to a coupled coincidence point result for a pair of compatible mappings. A control function has been used in our theorem. The mappings are assumed to satisfy a weak contractive inequality. Our theorem improves the results of Harjani et al. (Nonlinear Anal. TMA 74:1749–1760, 2011). The result we have established is illustrated with an example which also shows that the improvement is actual.     

无穷时滞脉冲方程的一致渐近稳定性

本文利用Liapunov泛函与Liapunov函数方法建立了无穷时滞脉冲泛函微分方程基于两种测度的一致稳定和一致渐近稳定的一个新的定理,并通过实例说明了所获结论的应用.     

A bifurcation theorem for nonlinear matrix models of population dynamics

ABSTRACT

We prove a general theorem for nonlinear matrix models of the type used in structured population dynamics that describes the bifurcation that occurs when the extinction equilibrium destabilizes as a model parameter is varied. The existence of a bifurcating continuum of positive equilibria is established, and their local stability is related to the direction of bifurcation. Our theorem generalizes existing theorems found in the literature in two ways. First, it allows for a general appearance of the bifurcation parameter (existing theorems require the parameter to appear linearly). This significantly widens the applicability of the theorem to population models. Second, our theorem describes circumstances in which a backward bifurcation can produce stable positive equilibria (existing theorems allow for stability only when the bifurcation is forward). The signs of two diagnostic quantities determine the stability of the bifurcating equilibrium and the direction of bifurcation. We give examples that illustrate these features.     

一类捕食者-食饵模型的稳定性及Hopf分支

研究一类具有时滞和阶段结构的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件.利用规范型和中心流形定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.     

X-调和映射的稳定性

在一般调和映射基础上定义了X-调和映射和次椭圆调和映射，得到了X-调和映射的稳定性定理，它是Leung一般调和映射及其稳定性定理的推广．     

具有可变时滞的非线性非自治差分方程的线性化全局渐近稳定性及其应用

证明了在一定条件下,具有可变时滞的非线性非自治差分方程的全局渐近稳定性可由某种线性差分方程的渐近稳定性确定,给出了这类差分方程全局渐近稳定的充分条件.作为实例,获得了具有可变时滞的离散型非自治广义Log istic方程的全局吸收性判别准则.     

广义Phillips模式非线性不稳定的饱和问题(Ⅱ)——扰动能量及位涡拟能的下界估计

在Arnol'd第二定理的范围内进一步讨论广义Phillips模式非线性不稳定的饱和问题,得到了基流不稳定时扰动能量及位涡拟能的下界估计。     

Stability of impulsive systems depending on a parameter

In this paper, we present a practical exponential stability result for impulsive dynamic systems depending on a parameter. Stability theorem and converse stability theorem are established by employing the second Lyapunov method. These theorems are used to analyze the practical exponential stability of the solution of perturbed impulsive systems and cascaded impulsive systems, depending on a parameter. Copyright © 2015 John Wiley & Sons, Ltd.