基于Lyapunov指数的高炉铁水[Si]预报

通过对国内两座中型高炉冶炼过程的[S i]时间序列的混沌分析,计算出相应的Lyapunov指数谱.由最大Lyapunov指数为正,定量的说明了两座高炉冶炼过程具有混沌性,并估计了两座高炉冶炼过程[S i]可预测的时间尺度.同时根据最大Lyapunov指数,建立了高炉冶炼过程[S i]预报模型,取得了较好的结果.     

Cohen-Grossberg神经网络指数稳定性的新判则

避免构造Lyapunov函数的困难,运用广义Dahlquist数方法研究了Cohen- Grossberg神经网络模型的指数稳定性,不但得到了Cohen-Grossberg神经网络平衡点存在惟一性和指数稳定性的全新充分条件,而且给出了神经网络的指数衰减估计.与已有文献结果相比,所得的神经网络指数稳定的充分条件更为宽松,给出的解的指数衰减速度估计也更为精确.     

Liu系统的Lyapunov维数估计

基于Leonov提出的Lyapunov维数理论,通过构造合适的Lyapunov函数,给出了Liu系统不变集的Lyapunov维数估计式.最后并给出了Liu系统混沌吸引子的Lyapunov维数估计.     

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.     

带跳的线性SDE的上Lyapunov指数的逼近

在假设线性随机微分方程的Lyapunov上指数q存在的条件下，我们将线性随机微分方程离散化，获得了几种逼近线性随机微分方程解的Markov链，并且证明了这些Markov链存在Lyapunov指数q^h。当离散化步长h很小时，我们给出了误差|q—q^h|阶的理论估计，这是Talay[9]中相应结果的推广。     

磁盘发电机系统的动力学研究及其在混沌同步中的应用

摘要本文通过构造适当的Lyapunov函数,研究了磁盘发电机系统的最终有界集、正向不变集和全局指数吸引集,得到了该系统界的四维椭球估计表达式.然后将所得到的该系统界的估计应用到完全同步之中去,并做出了相应的数值模拟.     

Cohen-Grossberg神经网络的全局指数稳定性分析

本文研究了CohenGrossberg神经网络模型的指数稳定性.为避免构造Lyapunov函数的困难,我们采用广义相对Dalquist数方法来分析神经网络的稳定性.借助这一方法,我们不但得到了CohenGrossberg神经网络模型平衡解的存在性、唯一性和全局指数稳定性的新的充分条件,而且给出了神经网络的指数衰减估计.所获结论改进了已有文献的相关结果.     

动力系统实测数据的Lyapunov指数的矩阵算法

Lyapunov指数l是定量描述混沌吸引子的重要指标,自从1985年Wolf提出Lyapunov指数l的轨线算法以来,如何准确、快速地计算正的、最大的Lyapunov指数l_max便成为人们关注的问题,虽有不少成功计算的报导,但一般并不公开交流.在Zuo Bingwu理论算法的基础上,给出了Lyapunov指数l的具体的矩阵算法,并与Wolf的算法进行了比较,计算结果表明:算法能快速、准确地计算(主要是正的、最大的)Lyapunov指数l_max.并对Lyapunov指数l的大小所反应的吸引子的特性进行了分析,并得出了相应的结论.     

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.     

具有时滞特性种群增长模型的混沌控制

研究一类具有时滞离散种群增长模型的混沌控制问题.首先通过绘制分岔图和系统的Lyapunov指数图验证了系统在一定参数条件下表现为混沌状态,然后对此离散系统的Lyapunov指数进行配置,保证了系统正Lyapunov指数变为预设的负Lyapunov指数,最后设计控制器,数值仿真结果不仅验证其配置的有效性,而且保证能将系统快速地稳定到期望点上.     

A coupling approach to estimating the Lyapunov exponent of stochastic max-plus linear systems

This paper addresses the problem of approximately computing the Lyapunov exponent of stochastic max-plus linear systems. Our approach allows for an efficient simulation of bounds for the Lyapunov exponent. We provide sufficient conditions for the convergence of the bounds. In particular, a perfect sampling scheme for the Lyapunov exponent is established. We illustrate the effectiveness of our bounds with an application to (real-life) railway systems.     

Random logistic maps and Lyapunov exponents

We prove that under certain basic regularity conditions, a random iteration of logistic maps converges to a random point attractor when the Lyapunov exponent is negative, and does not converge to a point when the Lyapunov exponent is positive.     

Explicit examples of arbitrarily large analytic ergodic potentials with zero Lyapunov exponent

We give explicit examples of arbitrarily large analytic ergodic potentials for which the Schr?dinger equation has zero Lyapunov exponent for certain energies. For one of these energies there is an explicit solution. In the quasi-periodic case we prove that one can have positive Lyapunov exponent on certain regions of the spectrum and zero on other regions. We also show the existence of 1-dependent random potentials with zero Lyapunov exponent. Research partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT), Institutional Grant 2002-2052. Received: February 2005; Accepted: May 2005     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

Joint Continuity of Lyapunov Exponent for Finitely Smooth Quasi-periodic Schr?dinger Cocycles

We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schr?dinger cocycles with the C~2 cos-type potentials. In particular, the Lyapunov exponent is log-H?lder continuous at each Diophantine frequency.     

Analytical expression for zero Lyapunov exponent of chaotic noised oscillators

This paper is devoted to the analytical formula for zero Lyapunov exponent describing the dynamics of interacting chaotic systems with noise. The deduced analytical prediction is in a good agreement with the value of zero Lyapunov exponent obtained numerically for two unidirectionally coupled Rössler oscillators. We have shown that this good agreement is observed for a wide diapason of the values of the control parameters.     

Diagnostic of cardio-vascular disease with help of largest Lyapunov exponent of RR-sequences

We suggest to present a discrete sequence of cardiointervals in the form of a smooth time dependence and for the given time series compute the largest Lyapunov exponent. Processing the database with RR-intervals of patients suffering from coronary artery disease (CAD) has shown that the largest Lyapunov exponent can be a diagnostic criteria allowing one to distinguish between different groups of patients with more confidence than the standard methods for time series processing accepted in cardiology.     

Estimate on the Pathwise Lyapunov Exponent of Linear Stochastic Differential Equations with Constant Coefficients

In this article, we study the problem of estimating the pathwise Lyapunov exponent for linear stochastic systems with multiplicative noise and constant coefficients. We present a Lyapunov type matrix inequality that is closely related to this problem, and show under what conditions we can solve the matrix inequality. From this we can deduce an upper bound for the Lyapunov exponent. In the converse direction, it is shown that a necessary condition for the stochastic system to be pathwise asymptotically stable can be formulated in terms of controllability properties of the matrices involved.     

Hybrid feedback stabilization of quasilinear systems in the plane

We apply Artstein's hybrid feedback algorithm to stabilize quasilinear dynamical systems with complex multipliers in the plane. We study only the case of incomplete observation when ordinary feedback controls do not work. The main results of the paper state that Artstein's procedure provides an arbitrary rate of asymptotic convergence/divergence of solutions. In other words, we prove the complete controllability from below of the upper Lyapunov exponent and the uniform upper Lyapunov exponent for the quasilinear systems in question.