Calculation of Coefficients of Simplest Normal Forms of Hopf and Generalized Hopf Bifurcations

Consider the following dynamical system x.=f(x),x∈Rn(1)wherexis the state vector andfis analytic, assumingthatx=0 is an equilibrium of system (1), i.e.f(0) =0. Further, suppose that the Jacobian matrixevaluated on the equilibriumx=0 presents a purelyimag…     

Computation of the Simplest Normal Forms for Resonant Double Hopf Bifurcations System Based on Lie Transform

The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.     

一类具有对称性的幂零向量场的高阶规范形

规范形是研究非线性向量场的动分岔问题强有力的工具,它包含了原系统在平衡点附近的所有动力学特性.对于一类具有γ对称的线性部分Jacobian矩阵为幂零矩阵的非线性向量场,在Ushiki规范形理论的基础上,利用无穷小形变的方法,得到了一维和二维的幂零向量场的具有γ对称的三阶、五阶规范形,并推导和证明了具有γ对称的且1-节退化的向量场的k阶规范形.     

二维滞后Logistic系统的分岔与混沌研究

用数值模拟的方法研究了二维滞后Logistic系统。对于二维滞后Logistic系统的混沌的形成过程进行了探讨。理论分析了二维Logistic映射的分岔,用分岔图、Lyapunov指数图和发生Hopf分岔的点附近的相图,有选择地研究了控制参数空间中两条轨线变化时系统行为的演化.     

一种各向同性不可压超弹性材料球体的空穴分岔问题的研究

研究了各向同性不可压超弹性材料球体在表面均匀拉伸死载荷作用下的空穴分岔问题,得到了描述球体内部的空穴生成和增长的空穴分岔方程,证明了空穴分岔方程的平凡解支上存在唯一的分岔点,并给出了分岔的辨别条件;利用奇点理论给出了空穴分岔方程在分岔点的等价正规形,并利用最小势能原理讨论了空穴分岔方程的稳定性。     

三阶非线性泛函微分方程的振动性和渐近性

利用广义Riccati变换和平均不等式技巧,研究了一类三阶非线性泛函微分方程的振动性和渐近性,建立了所述方程一切解振动或者收敛于零的两个新的充分条件,推广和改进了一些文献中的结果．     

高维四轮转向汽车侧向动力学系统的稳定性分析

引入二次多项式平方轮胎模型,选取合适的状态变量,建立了四轮转向汽车四维非线性动力学系统,应用中心流形定理对其进行了降维处理并转换为中心流形上的一阶约化系统.应用非线性分岔和稳定性理论对均匀路面工况的稳定性进行了分析,并在Matlab/Simulink中进行了仿真.结果表明：随着车速和前轮转角的增加,高维四轮转向汽车奇异点处会发生鞍结分岔,该分岔会导致汽车失稳.     

Kuramoto-Sivashinsky 方程中定常解分歧到旋转波解的一个注记

In this paper, we consider the detection and calculation of bifurcation from nontrivial steady-state solutions to ro~ wave solutions of the Kttramoto-Sivashinsky（K-S） equation by using the nonlinear Galerkin method. Numerical results show the efficiency and advantages of the nonlinear Galerkin method over the conventional Galerkin method in this application.     

模糊规则的表示方法研究

在已有的各种推理方法中,所使用的产生式规则表示形式都不统一,其中含有的信息量也不一样,有的少,有的多,各有侧重点,但都不全面,因而不能把它们作为模糊知识的统一表示形式．其根本的原因就是推理模型本身不完备．本文描述的通用模糊规则,是建立在通用不确定模型和模糊集合理论的基础之上的知识统一表示形式,也是通用模糊推理算法的基础．这种方法采用可能性分布理论来表示知识的模糊性,对一般规则表示进行全面的模糊化,全面考虑了知识的模糊性．它含有推理所需的丰富信息,能用于表达各种情况的模糊性,有着广泛的适用性．已有的规则形式,如确定性知识的规则表示等,只是这种通用形式在忽略部分模糊性情况下的特例．这种表示方法在飞机总体外形设计模糊专家系统（ＡＣＤＳ－ＦＥＳ）中得到了很好的运用．     

模糊规则的表示方法研究

在已有的各种推理方法中，所使用的产生式规则表示形式都不统一，其中含有的信息量也不一样，有的少，有的多，各有侧重 点，但都不全面，因而不能把它们作为模糊知识的统一表示形式.其根本的原因就是推理模型本身不完备.本文描述的通用模糊规 则，是建立在通用不确定模型和模糊集合理论的基础之上的知识统一表示形式，也是通用模糊推理算法的基础.这种方法采用可 能性分布理论来表示知识的模糊性，对一般规则表示进行全面的模糊化，全面考虑了知识的模糊性.它含有推理所需的丰富信息， 能用于表达各种情况的模糊性，有着广泛的适用性.已有的规则形式，如确定性知识的规则表示等，只是这种通用形式在忽略部分 模糊性情况下的特例.这种表示方法在飞机总体外形设计模糊专家系统(ACDS-FES)中得到了很好的运用.     

非线性薛定谔方程的稳态解及其稳定性研究

用行波变换方法和分叉理论研究里非线性薛定谔方程的定常解和定常解的稳定性.计算结果表明:非线性薛定谔方程存在两类定常解,静态解和平面波解.对于具有正阻尼和软特性的非线性薛定谔方程,稳定的平面解存在于正常色散媒质中;而对于具有正阻尼和硬特性的非线性薛定谔方程,稳态平面波解只存在于反常色散媒质中.此外,非线性薛定谔方程在行波变换下的派生系统在处发生Hopf分叉.     

A Comparative Study of the Effects of Recency of Instruction on the Stability of IRT and Conventional Item Parameter Estimates

A potential concern for individuals interested in using item response theory (IRT) with achievement test data is that such tests have been specifically designed to measure content areas related to course curriculum and students taking the tests at different points in their coursework may not constitute samples from the same population. In this study, data were obtained from three administrations of two forms of a Biology achievement test. Data from the newer of the two forms were collected at a spring administration, made up of high school sophomores just completing the Biology course, and at a fall administration, made up mostly of seniors who completed their instruction in the course from 6–18 months prior to the test administration. Data from the older form, already on scale, were collected at only a fall administration, where the sample was comparable to the newer form fall sample. IRT and conventional item difficulty parameter estimates for the common items across the two forms were compared for each of the two form/sample combinations. In addition, conventional and IRT score equatings were performed between the new and old forms for each o f the form sample combinations. Widely disparate results were obtained between the equatings based on the two form/sample combinations. Conclusions are drawn about the use o f both classical test theory and IRT in situations such as that studied, and implications o f the results for achievement test validity are also discussed     

一类可压缩超弹性球体的空穴的生成和增长

In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term.Void formation and growth in the interior of a sphere composed of compressible hyper-elastic material, subjected to a prescribed uniform displacement, was examined.A parametric cavitated bifurcation solution for the radial deformed function was obtained.Stability of the solution of the cavitated bifurcation equation was discussed.With the appearance of a cavity, an interesting feature of the radial deformation near the deformed cavity wall is the transition from extension to compression.     

混流式水轮机调节系统非线性建模与分叉分析

基于Matlab仿真软件,考虑弹性水击对水轮机调节系统的影响,建立弹性水击水轮机微分代数模型,并与调速器和发电机共同构成水轮机调节系统非线性模型。在此基础上运用非线性动力学分叉理论对PID调速器参数进行Hopf分叉行为研究,得出PID参数三维分叉曲面、二维分叉曲线及稳定域,并通过对时域图、相轨迹图等的综合分析,得到取不同调速器参数时系统的非线性动力学特性,为机组PID参数选择提供理论依据。最后通过系统仿真得出,在小扰动下线性模型和非线性模型均能适用,在大扰动下非线性模型能更真实地反映机组动态特性。     

Void Formation and Growth for a Class of Compressible Hyper-Elastic Sphere

In this paper, the strain energy function proposed by Shang and Cheng was generalized by introducing a nonlinear term. Void formation and growth in the interior of a sphere composed of compressible hyper-elastic material, subjected to a prescribed uniform displacement, was examined. A parametric cavitated bifurcation solution for the radial deformed function was obtained. Stability of the solution of the cavitated bifurcation equation was discussed. With the appearance of a cavity, an interesting feature of the radial deformation near the deformed cavity wall is the transition from extension to compression.     

非解析径向轴承支承转子系统非线性动力特性分析

Nomenclaturex,y,x ·, y·-displacement and velocity of rotor-x,-y,x-·,-y·-displacement and velocity of rotor , di mension less¨x,¨y-acceleration of rotor¨-x,¨-y-acceleration of rotor ,di mensionlessω-rotating speed of rotor-ω-rotating speed of rotor ,di mensionlessx,y,z-Cartesian coordinates-x,-y,-z-Cartesian coordinates ,di mensionless2m-mass of rotorg-acceleration of gravityG-weight of rotor ,di mensionlesse=e2x e2y-mass eccentricity of rotorex,ey-mass eccentricity of rotor in thexan…     

一类具振动系数的偶数阶非线性中立型方程的振动性

研究了一类具振动系数的偶数阶非线性中立型微分方程,通过利用广义Riccati变换和引入参数函数,得到了该类方程振动的若干充分条件,所得结果推广了已有的相应结论。     

二阶微分方程解的导函数比较定理

利用文中建立的两个微分恒等式研究了两类非线性微分方程解的导函数的零点比较定理及振动比较定理，推广了一些已知结论。     

Young Children's Human Figure Drawing: cross‐sectional and longitudinal studies

Abstract Forty‐two children aged between 2 years and 4 years 11 months were asked to draw a person. Their drawings were categorised as (1) scribbles, (2) distinct forms, (3) tadpoles, (4) transitional and (5) conventional figures. The first representational figures, the tadpoles, appeared at an average age of 3 years 1 month. It was predicted that if tadpole figures result from the complexity of the task rather than from a conceptual difficulty then tasks with reduced demands (a copying task, a jig‐saw task, and a dictation task) should facilitate the drawing of conventional figures. In fact, few conventional figures were produced and the tadpole form was highly resistant across the different tasks.

Six of the children were followed longitudinally over a one‐year period from a pre‐representational to a conventional stage of human figure drawing. Spontaneous drawings as well as drawings from six test sessions were collected in order to check whether all children drew ‘tadpole’ forms before they produced conventional figures and whether the conventional figures were adapted from the tadpoles. Four of the children did produce tadpole forms; two did not, but were probably specifically tutored in the conventional form by a peer or parents. There were wide individual differences in the nature of the transition from one form to the next, but there was no clear evidence that the conventional figure had been adapted from the tadpole form.     

基于有限滞时的免疫系统的稳定性与分支解

以时滞τ为参数,利用特征根法分析平衡点的稳定性,得到稳定性存在的范围及在平衡点处产生hopf分支的条件,再利用中心流形定理和规范型理论,得到hopf周期解的稳定性及计算公式,为数值模拟提供依据.