目标函数扰动的集值优化问题的稳定性

本文研究了由目标函数扰动的集值优化问题的有效点集所定义的集值映射的半连续性.讨论了目标函数扰动的集值优化问题在上半连续意义下的稳定性.特别地,在广义适定性条件下,证明了集值优化问题在上半连续意义下的稳定性.     

约束锥扰动多目标规划锥有效解集的闭性和半连续性

本文研究拓扑向量空间中目标映射和约束映射均为连续,约束映射的约束锥为半连续的条件下,受扰动可达目标集的锥有效点集和锥弱有效点集的闭性、半连续性和锥半连续性.在此基础上,得到了约束锥扰动多目标规划问题的锥有效解集和锥弱有效解集的闭性和半连续性.     

无单调性集值变分不等式的一种投影算法

本文给出了求解无单调性集值变分不等式的一个新的投影算法,该算法所产生的迭代序列在Minty变分不等式解集非空且映射满足一定的连续性条件下收敛到解.对比文献[10]中的算法,本文中的算法使用了不同的线性搜索和半空间,在计算本文所引的两个数值例子时,该算法比文献[10]中的算法所需迭代步更少.     

广义扰动映射的上导数

主要讨论了两集值映射和的上导数．在比标准约束品性弱的条件下得到了两个集值映射和的上导数与两集值映射上导数的和之间的包含关系,并将此结论用于讨论广义扰动映射的上导数,得到广义扰动映射的上导数的上界估计．     

渐近上半紧的多值随机半流的随机吸引子

该文研究多值随机半流的随机吸引子的存在性．首先证明在拉回渐近上半紧及吸收的条件下,关于极限集的一个抽象结果,然后证明了随机的吸引子的存在性．     

空间离散Fitz-Hugh-Nagumo方程和双稳反应扩散方程组的渐近行为

本文利用扰动方法,研究了Ｆitz-Hugh-Ngaumo方程和双稳反应扩散方程在Neuman边值条件下空间离散后的渐近行为,证明了两个格微分方程组的不变区域、吸引集和整体吸引子的存在性,并给出了离散Ｆitz-Hugh-Ngaumo方程的整体吸引子的Hausdorff维数估计。     

非自治集值映射的渐近性态

本文研究了非自治集值映射的渐近性态,利用非自治集值映射的上链性质,得到了在一定条件下非自治集值映射的上链吸引子的存在唯一性.     

基于拓扑博弈的集值映射的通有锥度量连续性

本文利用拓扑博弈的方法,研究了非紧值锥C度量半连续集值映射的通有锥C度量连续性问题,证明了从拟完备空间到线性度量空间的锥C度量上(下)半连续集值映射具有通有锥C度量连续性,利用锥C度量半连续性给出了拓扑空间为Baire空间的充分条件,结果包含了经典的关于紧值集值映射的Fort定理等相关结果.     

参数集值变分不等式的解映射的有界性和连续性

本文借助于非空闭凸集序列的外极限集和极大单调集值映射的外极限研究了参数集值变分不等式的集值解映射的有界性和外半连续性．     

一个标量泛函的研究及其在集值优化问题中的应用

本文在K条件下,研究了所给标量泛函的连续性和拟凸性,并利用该标量泛函,将集值优化问题转化为均衡问题,进而研究了含约束的集值优化问题弱充分解的存在性和拟集值优化问题强逼近解映射的上半连续性与下半连续性.与最近的文献相比,我们的方法是新的,条件和结论也更具一般性.     

Upper semicontinuity of pullback attractors for multi-valued random cocycle

In this paper we study the upper semicontinuity of random attractors for multi-valued random cocycle when small random perturbations approach zero or small perturbation for random cocycle is considered. Furthermore, we consider the upper semicontinuity of random attractors for multi-valued random cocycle under the condition which the metric dynamical systems is ergodic.     

The Shunted Homopolar Dynamo—An Analytic Approach to a Poincaré Map

We study the set of ordinary differential equations governing the homopolar disk dynamo. It is found that this set, which is a modification of the Lorenz system, has strange attractors of Lorenz type when R (which corresponds to the Rayleigh number of the Lorenz system) tends to infinity. A central aspect of this study is that the Poincare map for this limit can be obtained through Melnikov's perturbation method, in contrast to the usual dependence on numerical computation.     

Fractional standard map: Riemann–Liouville vs. Caputo

Properties of the phase space of the standard maps with memory obtained from the differential equations with the Riemann–Liouville and Caputo derivatives are considered. Properties of the attractors which these fractional dynamical systems demonstrate are different from properties of the regular and chaotic attractors of systems without memory: they exist in the asymptotic sense, different types of trajectories may lead to the same attracting points, trajectories may intersect, and chaotic attractors may overlap. Two maps have significant differences in the types of attractors they demonstrate and convergence of trajectories to the attracting points and trajectories. Still existence of the most remarkable new type of attractors, “cascade of bifurcation type trajectories”, is a common feature of both maps.     

Weak Pullback Attractors of Non-autonomous Difference Inclusions

Weak pullback attractors are defined for non-autonomous difference inclusions and their existence and upper semi continuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for (at least) a single trajectory rather than all trajectories at each starting point. The concept is thus useful, in particular, for discrete time control systems.     

Weak pullback attractors of setvalued processes

Weak pullback attractors are defined for nonautonomous setvalued processes and their existence and upper semicontinuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for at least one trajectory rather than all trajectories at each starting point. The concept is useful in, for example, continuous time control systems and is related to that of viability.     

Robust invariant stabilization of nonlinear continuous and discrete systems

Two classes of continuous systems described by differential equations in which coefficients are functions of the state vector are considered. The systems are subject to two scalar controls and a constantly acting scalar perturbation.An analytical synthesis of a control is performed under which the system is invariant in the sense that the scalar output of the system approaches zero as time tends to infinity and does not depend on the perturbation; moreover, the limit norm of the state vector is bounded above by the least upper bound for the norm of perturbation. The case where the coefficients of the system are subject to an uncontrolled additive perturbation is considered. In this case, the limit of the output norm is bounded above by a known function of the perturbation value. The method of synthesis is based on constructing the Lyapunov function as a positive definite quadratic form with Jacobian matrix.     

Coderivatives of the generalized perturbation maps

This paper is devoted to considering the coderivatives of the generalized perturbation maps in general Banach spaces. Under some mild conditions, the upper estimate of coderivatives of the generalized perturbation maps are obtained. Their exact calculus rules are obtained under some additional conditions. Furthermore, the generalized perturbation maps are shown to be differentiably regular under some strong conditions.     

Self-similar sets satisfying the common point property

A self-similar set is a fixed point of iterated function system (IFS) whose maps are similarities. We say that a self-similar set satisfies the common point property if the intersection of images of the attractor under the maps of the IFS is a singleton and this point has a common pre-image, under the maps of the IFS, and the pre-image is in the attractor.Self-similar sets satisfying the common point property were introduced in Sirvent (2008) in the context of space-filling curves. In the present article we study some basic topological and dynamical properties of self-similar sets satisfying the common point property. We show examples of this family of sets.We consider attractors of a sub-IFS, an IFS formed from the original IFS by removing some maps. We put conditions on this attractors for having the common point property, when the original IFS have this property.     

一类非线性混沌系统混沌吸引子的冲击控制

在国内外研究工作的基础上,给出了一类非线性混沌系统混沌吸引子的冲击控制方案,运用普适方程的冲击控制理论导出了这类混沌系统混沌吸引子的冲击控制渐进稳定的条件,利用这一条件给出了混沌吸引子渐进稳定冲击控制的区间上界,最后给出了许多数据结果,这些结果对于混沌吸引子的控制将有重要的参考价值．