Nonlocal stochastic differential equations with time-varying delay driven by G-Brownian motion

This article studies a class of nonlocal stochastic differential equations driven by G-Brownian motion (G-NSDEs for short). We show the existence and uniqueness results of solutions by means of fixed point theorem. In addition, exponential estimation of (1) has been discussed. Furthermore, we present global solution to Equation (1) with the help of G-Lyapunov functional and ψ-type function.     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.     

三维四翼广义增广Lü系统

增广Lü系统是仅含有两个控制参数的三维混沌系统,可产生一个伪四翼吸引子.利用混沌反控制方法,通过在增广Lü系统中引入一个简单的线性状态控制器,提出了一个新三维混沌系统——广义增广Lü系统.新系统实现了一个真正的具有复合结构的四翼吸引子,它包含了两个镜像对称的子系统.理论分析、数值仿真和电路实验证明了广义增广Lü系统四翼吸引子的存在性,也阐述了广义增广Lü系统有着较增广Lü系统更加丰富的动力学特性. 关键词： 广义增广Lü系统 四翼吸引子 数值仿真 电路实验     

Attractors of derivative complex Ginzburg-Landau equation in unbounded domains

The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ² is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in ℝ² is detailed studied.      

逐步增加的Ⅱ型截尾下系统可靠性的Bayes分析及寿命预测

在逐步增加的型截尾模型下,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的Bayes估计及单样本场合未来观测值的预测问题.在两个参数均未知的情形下,分别在平方损失(SE)、LINEX损失和熵(General Entropy,GE)损失函数下给出两个参数及可靠性指标的Bayes估计,对于超参数的确定,给出一种新的方法;并讨论了单样本场合未来观测值的预测问题,给出预测分布及预测区间;最后利用随机模拟方法进行比较,并对结果进行了讨论.     

具常数存放的非线性功能反应捕食模型的定性分析

研究一类食饵具常数存放且功能反应函数为次线性函数的食饵-捕食者模型,获得了一些平衡点全局渐近稳定,极限环存在惟一的充分条件.利用数值仿真检验了我们的结论.     

一类具有脉冲效应的食饵依赖捕食系统分析

基于害虫防治,该文提出了一类具有脉冲效应的食饵依赖捕食系统并进行了分析,根据Floquet乘子理论,我们获得了害虫根除周期解全局渐近稳定与系统持续生存条件.     

非线性最小二乘问题的信赖域方法

本文提出一个新的非线性最小二乘的信赖域方法,在该方法中每个信赖域子问题只需要一次求解,而且每次迭代的一维搜索步长因子是给定的,避开一维搜索的环节,大大地提高了算法效率.文中证明了在一定的条件下算法的全局收敛性.     

Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey

We consider nonlinear partial differential equations with several Fuchsian variables of type , where is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variable . The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.

     

食饵具有阶段结构的捕食-食饵系统的动力学行为

In this paper,we considered the predator-prey system with stage-structure for prey,where the predators predate immature preys only.The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed,and then uniformly persistent sufficient conditions of populations were found.