Attracting and invariant sets for a class of impulsive functional differential equations

In this article, a class of nonlinear and nonautonomous functional differential systems with impulsive effects is considered. By developing a delay differential inequality, we obtain the attracting set and invariant set of the impulsive system. An example is given to illustrate the theory.     

Cohen-Grossberg-type BAM神经网络吸引集和不变集(英文)

利用矩阵理论和不等式分析技巧,讨论了一类具分布时滞的Cohen-Grossberg型BAM神经网络的不变集和吸引集,获得了一些最新结果,并给出一个实例说明我们结果的可行性.     

Density of hyperbolicity and tangencies in sectional dissipative regions

In this paper we extend the notion of sectionally dissipative periodic points to arbitrarily compact invariant sets. We show that given a sectionally dissipative and attracting region for a diffeomorphisms f, there is a neighborhood of f and a dense subset of it such that any diffeomorphism g in this dense subset either exhibits a sectional dissipative homoclinic tangency or the part of the limit set of g in this attracting region is a hyperbolic compact set. The proof goes extending some results on dominated splitting obtained for compact surfaces maps.     

On Random Attractors for Mixing Type Systems

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system.     

具有变时滞Hopfield型神经网络的正不变集与吸引集

研究了具有变时滞Hopfield型神经网络的正不变集与吸引集，获得了正不变集与吸引集存在性的充分判据。     

Intermittency generated by attracting and weakly repelling fixed points

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.     

Eigen fuzzy sets and fuzzy relations

When R is a fuzzy relation between the elements of a finite set X, the fuzzy sets A of X such that R ° A = A (MAX-MIN composition) are called eigen fuzzy sets. The main result of this paper is the determination of the greatest eigen fuzzy set associated with a given fuzzy relation and we give three methods illustrated by an example. We then state that the greatest eigen fuzzy set associated with $\text{R}\text{?}$, the transitive closure of R, is exactly the one associated with R. Finally we describe how to obtain all fuzzy relations keeping invariant a given fuzzy set.     

基于模糊不变子群的上、下近似

研究群中集合的粗糙近似问题。利用分解定理和表现定理,定义了群中集合关于模糊不变子群的上、下近似,并给出了近似算子的性质。证明了子群的上、下近似在同态映射下的不变性质。     

L-fuzzy代数的刻画

鉴于[2]中已有fuzzy代数结合的不理想，谷文祥和卢荼在L－fuzzy集论中重新定义了L－fuzzy代数，得到了一些理想的结论。但却没有给出它的截集式刻画。本文的目的就是借助于L－fuzzy集的几种水平截集给出了它的几个等价刻画，使得它的表现更为直观且更便于应用。最后，作为应用，本文简洁地证明了L－fuzzy代数在代数同态下是不变的和逆不变的。     

关于求解Fuzzy矩阵方程的注记

定义了 Fuzzy矩阵 A的同解简化矩阵 A( 2 ) ,利用同解简化矩阵 A( 2 ) 给出了 Fuzzy矩阵方程的简化解法 ,指出了文 [4]中定理 3的错误 .     

Attracting graphs of skew products with non-contracting fiber maps

We study attracting graphs of step skew products from the topological and ergodic points of view where the usual contracting-like assumptions of the fiber dynamics are replaced by weaker merely topological conditions. In this context, we prove the existence of an attracting invariant graph and study its topological properties. We prove the existence of globally attracting measures and we show that (in some specific cases) the rate of convergence to these measures is exponential.

     

Attracting current and equilibrium measure for attractors on ℙ<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>

Let f be a holomorphic endomorphism of ℙ ^k having an attracting setA. We construct an attracting current and an equilibrium measure associated toA. The attracting current is weakly laminar and extremal in the cone of invariant currents. The equilibrium measure is mixing and has maximal entropy onA.     

Content-based image retrieval using visually significant point features

This paper presents a new image retrieval scheme using visually significant point features. The clusters of points around significant curvature regions (high, medium, and weak type) are extracted using a fuzzy set theoretic approach. Some invariant color features are computed from these points to evaluate the similarity between images. A set of relevant and non-redundant features is selected using the mutual information based minimum redundancy-maximum relevance framework. The relative importance of each feature is evaluated using a fuzzy entropy based measure, which is computed from the sets of retrieved images marked relevant and irrelevant by the users. The performance of the system is evaluated using different sets of examples from a general purpose image database. The robustness of the system is also shown when the images undergo different transformations.     

Fuzzy invariant subgroups and fuzzy ideals

The purpose of this paper is to introduce some basic concepts of fuzzy algebra, as fuzzy invariant subgroups, fuzzy ideals, and to prove some fundamental properties. In particular, it will give a characteristic of a field by a fuzzy ideal.     

Fixed Point Index in Hyperspaces: A Conley-Type Index for Discrete Semidynamical Systems

Let X be a locally compact metric absolute neighbourhood retractfor metric spaces, U X be an open subset and f: U X be a continuousmap. The aim of the paper is to study the fixed point indexof the map that f induces in the hyperspace of X. For any compactisolated invariant set, K U, this fixed point index produces,in a very natural way, a Conley-type (integer valued) indexfor K. This index is computed and it is shown that it only dependson what is called the attracting part of K. The index is usedto obtain a characterization of isolating neighbourhoods ofcompact invariant sets with non-empty attracting part. Thisindex also provides a characterization of compact isolated minimalsets that are attractors.     

Lifting measures to Markov extensions

Generalizing a theorem ofHofbauer (1979), we give conditions under which invariant measures for piecewise invertible dynamical systems can be lifted to Markov extensions. Using these results we prove:

1. IfT is anS-unimodal map with an attracting invariant Cantor set, then ∫log|T′|dμ=0 for the unique invariant measure μ on the Cantor set.
2. IfT is piecewise invertible, iff is the Radon-Nikodym derivative ofT with respect to a σ-finite measurem, if logf has bounded distortion underT, and if μ is an ergodicT-invariant measure satisfying a certain lower estimate for its entropy, then μ?m iffh _μ (T)=Σlogf dμ.

     

Structural stability on basins for numerical methods

In this paper, we show that a flow with a hyperbolic compact attracting set is structurally stable on the basin of attraction with respect to numerical methods. The result is a generalized version of earlier results by Garay, Li, Pugh, and Shub. The proof relies heavily on the usual invariant manifold theory elaborated by Hirsch, Pugh, and Shub (1977), and by Robinson (1976).

     

基于∨-·运算的Fuzzy矩阵方程的摄动问题

定义基于∨ - .运算的 Fuzzy矩阵 A的同解简化矩阵 ,利用 A的同解简化矩阵 A(1) 给出基于∨ - .运算的 Fuzzy矩阵方程的矩阵解法 ,并研究这类 Fuzzy矩阵方程的摄动问题。     

Dimension and local structures of attracting manifolds of smooth dynamical systems

We give a numerical algorithm to compute the dimension and local structures of attracting sets or invariant manifolds of smooth dynamical systems. This algorithm is based on local adaptive Galerkin bases and is tested for several examples. The important degrees of freedom that are preferentially selected, from the geometrical point of view, are found.     

Banach空间上泛函微分方程的渐近性

§ 1　IntroductionIn the last few years,invariant sets and attractors of (functional) differentialequations have been extensively discussed and various interesting results on the invariantsets and attractors,and estimates on the basin of attraction have been reported(see,forinstance,[1 ,2 ,4,6,1 0 ,1 3 ,1 5,1 8] ) .However,not much hasbeen developed in the directionof giving criteria on the existence of invariant sets and attractors for the functionaldifferential equations even though there ar…