Adaptive Q–S synchronization between coupled chaotic systems with stochastic perturbation and delay

This work investigates the adaptive Q–S synchronization of coupled chaotic (or hyper-chaotic) systems with stochastic perturbation, delay and unknown parameters. The sufficient conditions for achieving Q–S synchronization of two stochastic chaotic systems are derived based on the invariance principle of stochastic differential equation. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the stochastic Q–S synchronization of non-identical chaotic (or hyper-chaotic) systems is to be obtained. Finally, two illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme.     

Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model

In the study of the Sparre Andersen risk model with phase‐type (n) inter‐claim times (PH (n) risk model), the distinct roots of the Lundberg fundamental equation in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundberg matrix L_δ(s) play important roles. In this paper, we study the case where the Lundberg fundamental equation has multiple roots or the corresponding eigenvectors are linearly dependent in the PH (n) risk model. We show that the multiple roots of the Lundberg fundamental equation det[L_δ(s)] = 0 can be approximated by the distinct roots of the generalized Lundberg equation introduced in this paper and that the linearly dependent eigenvectors can be approximated by the corresponding linearly independent ones as well. Using this result we derive the expressions for the Gerber–Shiu penalty function. Two special cases of the generalized Erlang(n) risk model and a Coxian(3) risk model are discussed in detail, which illustrate the applicability of main results. Finally, we consider the PH(2) risk model and conclude that the roots of the Lundberg fundamental equation in the right half of the complex plane are distinct and that the corresponding eigenvectors are linearly independent. Copyright © 2011 John Wiley & Sons, Ltd.     

对流扩散方程一类改进的特征线修正有限元方法

１引言在地下水污染,地下渗流驱动,核污染,半导体等问题的数值模拟中,均涉及抛物型对流扩散方程（或方程组）的数值求解问题．这些对流扩散型偏微分方程（或方程组）具有共同的特点：对流的影响远大于扩散的影响,即对流占优性,对流占优性给问题的数值求解带来许多困难,因此对流占优问题的有效数值解法一直是计算数学中重要的研究内容．用通常的差分法或有限元法进行数值求解将出现数值振荡．为了克服数值振荡,提出各种迎风方法和修正的特征方法并在这些问题上得到成功的实际应用、８０年代,Ｄｏｕｇｌａｓ和Ｒｕｓｓｅｌｌ［２］等…     

Solution and Application of the Matrix Equation AX~=b~

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＪ．ＪＢｕｃｋｌｅｙａｎｄＹ．ＱｕｈａｖｅａｌｒｅａｄｙｇｉｖｅｎｔｈｅｓｏｌｕｔｉｏｎｔｏｔｈｅｍａｔｒｉｘｅｑｕａｔｉｏｎＡｘ＝ｂｗｈｅｎｔｈｅｅｌｅｍｅｎｔｓｉｎＡａｎｄｂａｒｅｔｒｉａｎｇｕｌａｒｆｕｚｚｙｎｕｍｂｅｒｓ,Ａｉｓｓｑｕａｒｅａｎｄａｌｗａｙｓｎｏｎ－ｓｉｎｇｕ－ｌａｒ．Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅａｒｅｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅａｐｐｌｉｃａｔｉｏｎａｎｄｓｏｌｕｔｉｏｎｏｆｔｈｅｅｑｕａｔｉｏｎＡｘ＝ｂｗｈｅｎｔｈ…     

周期系数的高维Riccati方程的周期解

本文研究了周期系数的高维Riccati方程X’＝X·A（t）·X＋B（t）·X＋C（t）,其中X∈R(n×1)A（t）∈R(1×n),B（t）∈R(n×n),C（t）E∈R(n×1);A（t）,B（t）,C（t）均是以2π为周期的实连续矩阵或向量函数,建立了该方程存在广义周期解的一个充要条件和存在周期解的两个充分条件,推广了周期系数的Riccati方程存在周期解的一些结论．     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,...     

奇异摄动初值问题的一致收敛有限差分法

通过一阶和二阶导数讨论了带小参数的线性二阶常微分方程的初值问题.在均匀网格上得出了带常数拟合因子的指数型拟合差分格式,给出了离散最大模意义上的一阶一致收敛性.文中给出了数值结果.     

半无限带状各向异性材料的应力效应衰减估计

对带端面负载的半无限带状各向异性弹性材料建立了Saint-Venant原理.应用能量方法确立了应力效应衰减率的下界,得出了用各向异性材料的弹性常量表示的估计显式.最后,为了说明所得结果,对带端面负载、纤维偏离主轴的石墨-环氧树脂的衰减率给出数值实例.     

求解微分方程初值问题的一种弧长法

对于连续介质力学问题中导出的微分方程初值问题,常常具有解奇异性,如不连续、Ｓｔｉｆ性质或激波间断·本文通过在相应空间,引入一个或数个弧长参数变量,克服解的奇异性·对于常微分方程组引入弧长参数变量后,奇异性得以消除和削弱,应用一般的解常微分方程组的方法（如Ｒｕｎｇｅ＿Ｋｕｔａ法）求解·对于偏微分方程引入弧长参数变量后,在相应的空间离散成常微分方程组,用解奇异性常微分方程组相同的方法即可求解·本文给出了两个算例     

矩阵方程AXA^T＋BYB^T=C的双对称最小二乘解及其最佳逼近

基于共轭梯度法的思想,通过特殊的变形,建立了一类求矩阵方程AXA^T＋BYB^T=C的双对称最小二乘解的迭代算法．对任意的初始双对称矩阵．在没有舍人误差的情况下,经过有限步迭代得到它的双对称最小二乘解;在选取特殊的初始双对称矩阵时,能得到它的的极小范数双对称最小二乘解．另外,给定任意矩阵,利用此方法可得到它的最佳逼近双对称解,数值例子表明,这种方法是有效的．