一类具阻尼项的三阶非线性中立型泛函微分方程的振动性和渐近性

研究一类具阻尼项的三阶非线性中立型连续分布时滞泛函微分方程解的振动性和渐近性,利用广义Riccati变换、积分平均技巧和一些分析技巧,对α≠β的情况,建立了一组保证该方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则.     

Phase portraits of Abel quadratic differential systems of second kind with symmetries

We provide normal forms and the global phase portraits on the Poincaré disk of the Abel quadratic differential equations of the second kind having a symmetry with respect to an axis or to the origin. Moreover, we also provide the bifurcation diagrams for these global phase portraits.     

Two results on stable rapidly oscillating periodic solutions of delay differential equations

In 1999 Ivanov and Losson [A.F. Ivanov and J. Losson, Stable rapidly oscillating solutions in delay differential equations with negative feedback, Differ. Int. Eqns 12 (1999), pp. 811–832] presented a computer assisted proof that a particular delay differential equation (with negative feedback) admits a stable rapidly oscillating periodic solution (ROPS). In this article the delay equation of Ivanov and Losson is embedded in a five-parametric class of differential equations. Conditions on the parameters are given such that the delay equation admits a stable ROPS. Moreover, it is shown that for odd n?>?1 the delay equation admits a stable ROPS with n humps per unit time if the parameters satisfy some explicitly given conditions. The delay equation of Ivanov and Losson satisfies all conditions on the five parameters. This gives an analytic proof and a considerable generalization of the result of Ivanov and Losson. The conditions on the parameters are believed to be sharp in a certain sense. The second result proves part of a conjecture in Stoffer [D. Stoffer, Delay equations with rapidly oscillating stable periodic solutions, J. Dyn. Differ. Eqns 20(1) (2008), pp. 201–238]. For a class of stiff delay differential equations with piecewise constant nonlinearity (positive or negative feedback) and for every n the following holds: if the stiffness parameter is sufficiently large then there are 2a(n) essentially different stable ROPSs with n humps per time unit. a(n) is the number of essentially different binary n-stage shift register sequences.     

一类泛函微分方程多个周期正解的存在性

本文利用Krasnoselskii锥映象不动点定理讨论了某类一阶泛函微分方程周期正解的存在性、非存在性与多解,给出了方程至少有一个解,有两个解或无解的若干充分条件。所得结果改进并推广了文献中的部分工作。     

Limit cycles of resonant four-dimensional polynomial systems

We study the bifurcation of limit cycles from four-dimensional centres inside a class of polynomial differential systems. Our results establish an upper bound for the number of limit cycles which can be prolonged in function of the degree of the polynomial perturbation considered, up to first-order expansion of the displacement function with respect to small parameter. The main tool for proving such results is the averaging theory.     

An algorithm for computing a companion block diagonal form for a system of linear differential equations

In this paper we describe a new algorithm which reduces in a finite number of steps a linear system of differential equations to a companion block diagonal form. This form is particularly convenient if one wishes to compute invariants at singularities.     

一类时滞模型周期正解的存在性问题

利用非线性锥映射的拓扑度的性质，研究了一类时滞微分方程周期正解的存在性问题，并将所得结果应用于Nichloson's blowflies模型，证明了在周期环境下，Nicholson's blowflies模型方程存在周期正解。     

0.6 m段四个量级真空差分系统的实现

介绍了光谱辐射标准及计量测试光束线实验站上使用的，在0．6m段达到四个量级的真空差分而设计的差分系统。该系统在光束线和实验站运行时，要求在有限的长度范围内既要保证四个量级的真空差分效果又要让同步辐射光能顺利通过。文中详细介绍了该差分系统的理论计算、结构、实验结果与理论值的比较。讨论了引起理论值与实测值差异的几种原因。     

一类高阶中立型微分方程周期解的存在性

本文研究一类高阶中立型泛函微分方程周期解的存在性,利用一些分析技巧和k-集压缩映射理论得到了该类方程至少存在一个周期解的两类充分条件.所得结果将现有关于常微分方程的结论推广到了泛函微分方程情形,同时减少或减弱了已有结果中的一些条件,从方程的形式和周期解的存在性条件两个方面推广和改进了文献中的相应工作.     

电动力绳索系统的周期解求解及其稳定性分析

摘 要：对运行在倾斜圆轨道上的电动力绳索系统的动力学特性进行了分析研究。首先建立了系统的动力学模型,分别采用摄动法及推广后的数值算法求得系统的基本周期解,并运用所给数值算法中的稳定性判据分析了周期解的稳定性,得出该系统周期运动不稳定的结论。最后进行仿真验证,结果表明在摄动量较小时,两种求解算法得到的周期解基本相同,但当摄动量较大时,摄动法求得的周期解发生了畸变,不理想此时通常借助数值算法加以求解;仿真结果同样证实了所得周期解的不稳定特性。     

具有脉冲效应的Holling—Tanner捕食-被捕食系统的正周期解

为了描述突然性因素对捕食一被捕食系统的影响,本文建立了具有固定时刻脉冲影响的Holling-Tanner捕食-被捕食系统模型,研究了系统的正周期解的存在性.利用基于叠合度理论的连续定理,证明了模型的正T-周期解的存在性,给出了系统存在正周期解的条件,该条件由两个种群的内禀增长率、脉冲周期及一个脉冲周期内的脉冲影响总量给出,这说明脉冲影响可能导致种群系统的平衡状态发生改变.     

Updated semi‐discretization method for periodic delay‐differential equations with discrete delay

An updated version of the semi‐discretization method is presented for periodic systems with a single discrete time delay. The delayed term is approximated as a weighted sum of two neighbouring discrete delayed state values and the transition matrix over a single period is determined. Stability charts are constructed for the damped and delayed Mathieu equation for different time‐period/time‐delay ratios. The convergence of the method is investigated by examples. Stability charts are constructed for 1 and 2 degree of freedom milling models. The codes of the algorithm are also attached in the appendix. Copyright © 2004 John Wiley & Sons, Ltd.     

齐次微分方程通解的计算机求解

文章分析了解齐次方程及可以化为齐次方程的算法 ,编制了求齐次方程通解新的函数 d.solve的程序 ,并在奔腾 5 86机 ,MATL AB5 .1,5 .2上实例通过     

Application of generalized differential quadrature rule in Blasius and Onsager equations

The generalized differential quadrature rule (GDQR) proposed recently by the authors is applied here to third‐order non‐linear differential equations of the Blasius type and to sixth‐order linear Onsager differential equations. High (?3rd)‐order differential equations in fluid mechanics are dealt with without using δ‐point techniques. The half‐space domain is simplified in a practical way. Accurate results are obtained for both kinds of problems. The wide applicability of the GDQR in high‐order differential equations is manifested further through this work. Copyright © 2001 John Wiley & Sons, Ltd.     

A new nonlocal elasticity theory with graded nonlocality for thermo-mechanical vibration of FG nanobeams via a nonlocal third-order shear deformation theory

In the present research, free vibration study of functionally graded (FG) nanobeams with graded nonlocality in thermal environments is performed according to the third-order shear deformation beam theory. The present nanobeam is subjected to uniform and nonlinear temperature distributions. Thermo-elastic coefficients and nonlocal parameter of the FG nanobeam are graded in the thickness direction according to power-law form. The scale coefficient is taken into consideration implementing nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of nonlocal Euler–Bernoulli and Timoshenko beam models, and it is revealed that the proposed modeling can accurately predict the vibration frequencies of the FG nanobeams. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio, and thermal loading in detail. The present study is associated to aerospace, mechanical, and nuclear engineering structures that are under thermal loads.     

On liouvillian solutions of linear differential equations

This paper deals with the problem of finding liouvillian solutions of a homogeneous linear differential equationL(y)=0 of ordern with coefficients in a differential fieldk. For second order linear differential equations with coefficients ink _o(x), wherek _o is a finite algebraic extension ofQ, such an algorithm has been given by J. Kovacic and implemented. A general decision procedure for finding liouvillian solutions of a differential equation of ordern has been given by M.F. Singer, but the resulting algorithm, although constructive, is not in implementable form even for second order equations. Both algorithms use the fact that, ifL(y)=0 has a liouvillian solution, then,L(y)=0 has a solutionz such thatu=z/z is algebraic overk. Using the action of the differential galois group onu and the theory of projective representation we get sharp bounds (n) for the algebraic degree ofu for differential equations of arbitrary ordern. For second order differential equations we get the bound (2)=12 used in the algorithm of J. Kovacic and for third order differential equation we improve the bound given by M.F. Singer from 360 to (3)36. We also show that not all values less than or equal to (n) are possible values for the algebraic degree ofu. For second order differential equations we rediscover the values 2, 4, 6, and 12 used in the Kovacic Algorithm and for third order differential equations we get the possibilities 3,4, 6, 7, 9, 12, 21, and 36. We prove that if the differential Galois group ofL(y)=0 is a primitive unimodular linear group, then all liouvillian solutions are algebraic. From this it follows that, if a third order differential equationL(y)=0 is not of Fuchsian type, then the logarithmic derivative of some liouvillian solution ofL(y)=0 is algebraic of degree 3. We also derive an upper bound for the minimal numberN(n) of possible degreesm of the minimal polynomial of an algebraic solution of the riccati equation associated withL(y)=0.Supported by Deutsche Forschungsgemeinschaft while visiting North Carolina State University