广义Lorenz系统的全局指数吸引集及其应用

对于一种广义Lorenz系统,通过线性变换和构造广义Lyapunov函数,给出了全局指数吸引集估计的新方法,并给出了最终界的精确估计式.最后,将结果应用到Chen系统和Lü系统的混沌控制中,给出了保持系统指数稳定的一种线性反馈控制,并且反馈控制律具有更少的保守性.     

非自治变时滞Cohen-Grossberg网络的Lagrange稳定性和全局指数吸引集

基于考虑两种不同类型的激活函数,本文研究了非自治变时滞Cohen-Grossberg神经网络（CGNN）在Lagrange意义下的全局指数稳定性,通过利用新的不等式技巧和构造恰当的Lyapunov泛函给出非自治变时滞CGNN模型在Lagrange意义下全局指数稳定性（即一致有界性）以及对其全局指数吸引集估计的代数判据,并给出应用例子加以验证.     

有限个有理函数的随机复动力系统的Julia集

本文讨论有限个有理函数生成的随机复动力系统，得到Julia集有内点的充分条件和必要条件．证明了对任意的正数，可以构造有限个多项式，彼此的Julia集之间的距离大干L，但J(f1，…，fm)含有内点但不是全平面。     

统一混沌系统的全局指数吸引集的新结果

研究了参数α∈[1／29,14／173）时,统一混沌系统的全局指数吸引集问题．通过线性变换和广义Lyapunov函数方法,给出了系统最终上界的精确估计．所得结果发展和丰富了现有混沌系统吸引集的结果,并将在混沌控制和同步中得到广泛应用．     

ON THE INVERSE IMAGE SET OF RATIONAL FUNCTIONS

This article studies the inverse image of rational functions.Several theorems are obtained on the Julia set expressed by the inverse image,and a mistake is pointed out in H.Brolin' theorem incidentally.     

Equi-Attraction and Continuous Dependence of Strong Attractors of Set-Valued Dynamical Systems on Parameters

Equi-attraction properties of the global attractors of a family of set-valued dynamical systems {G_λ, λ∈Λ} with respect to a parameter λ∈Λ, where Λ is a compact metric space, are investigated. In particular, under appropriate conditions, it is shown that the equi-attraction of the family is equivalent to the continuity of in λ with respect to the Hausdorff distance. An example involving differential inclusions is given. Mathematics Subject Classifications (2000) Primary 47H17, 58F03, 34C20. Desheng Li: Supported by NNSF of China (10251002) and NNSF of Gansu province (3ZS041-A25-006).     

Cyclic invariant sets for one class of maps

We consider the dynamical system that is determined by a multidimensional map with scalar type nonlinearity and a nonnegative matrix of special form. For this map we establish the bifurcation character for the location of cyclic invariant sets in the phase space of the system, determine their location and periods depending on the properties of the matrix.     

关于随机动力系统的Fatou－Julia猜测

设Ｆ＝｛ｆ１，…，ｆＭ｝是一个次数大于１的多项式集合。我们证明了在一定条件下Ｆａｔｏｕ集Ｆ（Ｆ）没有游荡区域。更确切地说，对于Ｆ（Ｆ）的每一个分支Ω，存在整数ｍ≥０，ｎ≥０，ｍ≠ｎ和λ∈∑Ｍ使得Ｗｍα（Ω）和Ｗｎα（Ω）落入Ｆ（Ｆ）的同一分支     

带脉冲接种和时滞的乙肝模型的稳定性分析

建立了具有脉冲接种和总人口变化的时滞SEIR模型.证明了当R^*<1时染病者消亡即疾病最终消失,当R_*>1时将发展为地方病.     

随机动力系统的进展和问题

本文主要介绍随机动力系统的主要成果和进一步研究的问题。     

整函数迭代的稳定集

本文证明了低阶超越整函数的非游荡域有界;估计了超越整函数在其稳定集上的增长速度;给出了Ｊｕｌｉａ集的渐近方向分布的最佳密度估计。     

一类非线性抛物型变分不等方程的全局吸引子及弱近似惯性流形

对由一类非线性抛物型变分不等方程所描述的无穷维动力系统，给出了存在全局吸引子及弱近似惯性流形的充分条件．     

Basins of attractors of trajectories

We consider some examples of dynamical systems on compact spaces, which deal with the structure of sets of attraction of trajectories and formulate some problems implied by known results.     

Stochastic stability of generalized SRB measures of Axiom A basic sets

In this note we prove that the generalized SRB measure of an Axiom A basic set is stable under random diffeomorphisms type perturbations.

     

Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”, P. Yu,X.X. Liao,S.L. Xie,Y.L. Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886–2896]

In the commented paper the authors study some aspects of boundedness in the general Lorenz family, $\dot{x}=\sigma (y-x)\text{,}\dot{y}=\rho x-\gamma y-\mathit{xz}\text{,}\dot{z}=-\beta z+\mathit{xy}$, considering that it contains four independent parameters. However, as we show here by means of a linear scaling in time and coordinates, they are dealing with a system homothetically equivalent to the Lorenz system. Consequently, the novel and interesting results they provide for the general Lorenz family can be obtained working directly with the Lorenz equations, that is, dealing only with three independent parameters.     

Dependent sets of a family of relations of full measure on a probability space

For a probability space (X, B,μ) a subfamily F of theσ-algebra B is said to be a regular base if every B∈B can be arbitrarily approached by some member of F which contains B in the sense of the measure theory. Assume that {γr}γ∈Γis a countable family of relations of the full measure on a probability space (X,B,μ), i.e. for everyγ∈Γthere is a positive integer sγsuch that Rγ(?)Xsγwithμsγ(Rγ) = 1. In the present paper we show that if (X, B,μ) has a regular base, the cardinality of which is not greater than the cardinality of the continuum, then there exists a set K(?)X withμ*(K) = 1 such that (x1,...,xsγ)∈γr for anyγ∈Γand for any sγdistinct elements x1,..., xsγof K, whereμ* is the outer measure induced by the measureμ. Moreover, an application of the result mentioned above is given to the dynamical systems determined by the iterates of measure-preserving transformations.     

Attractors for Fully Discrete Finite Difference Scheme of Dissipative Zakharov Equations

A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions, the stability of the difference scheme and the error bounds of optimal order of the difference solutions are obtained in L²×H¹×H² over a finite time interval (0, T]. Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.