关于解的延拓定理之注解

在数学专业的常微分方程课程里有关解的存在唯一性、解的延拓和解对初值与参数的连续性构成了微分方程最基本的理论,这部分内容既是常微分方程的重点,又是该课程的难点.本文的目的是对解的延拓定理所涉及的概念和论证进行系统的梳理和完善,并希望能够弥补微分方程教材中的有关不足.     

ADIABATIC INVARIANTS OF SLOWLY VARYING THREE－DIMENSIONAL SYSTEMS AND EXISTENCE OF INVARIANT TORI OF LOTKA－VOLTERRA EQUATION

ＡＤＩＡＢＡＴＩＣＩＮＶＡＲＩＡＮＴＳＯＦＳＬＯＷＬＹＶＡＲＹＩＮＧＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＳＹＳＴＥＭＳＡＮＤＥＸＩＳＴＥＮＣＥＯＦＩＮＶＡＲＩＡＮＴＴＯＲＩＯＦＬＯＴＫＡ－ＶＯＬＴＥＲＲＡＥＱＵＡＴＩＯＮＬＩＪＩＢＩＮＺＨＡＯＸＩＡＯＨ...     

Fourier series of rational fractions of Jacobian elliptic functions

In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic functions sn(u.k.), cn(u.k) and dn(u.k) are listed, which cannot be found in the handbook^[1] and Ref. [2]. For the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method, and for study of some problems of physical science and engineering. these formulas can be used. Proiect Supported by the Science Fund of the Chinese Academy of Sciences.     

一类非线性振动方程的渐近分析

本文用KBM方法处理非线性振动方程x+(a|x|~λ+bx|x|~μ+C)x+x=0,并且找到了该方程稳定周期解.最后,给出了软弹簧Rayleigh方程x+(a|x|~λ+bx|x|μ+c)x+(x-β~2x~3)=0的相应结果.     

STABILITY OF SUBHARMONICS AND BEHAVIOUR OF BIFURCATIONS TO CHAOS ON TORAL VAN DER POL EQUATION

One of the basic problems in bifurcation theory is to understand the way in whichhorseshoes are created. In this paper, we study the bifurcation behavior exhibited by the toral Vander Pol equation subject to periodic forcing. Our attention is focased on routes relevant to horseshoestype chaos.     

Bifurcations of travelling wave solutions for Jaulent-Miodek equations

By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations,the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown.Under the given parametric conditions,all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained.     

一类耦合非线性波方程的行波解分支

利用动力系统的Hopf分支理论来研究耦合非线性波方程周期行波解的存在性和稳定性．应用行波法把一类耦合非线性波方程转换为三维动力系统来研究,从而给在不同的参数条件下给出了周期解存在和稳定性的充分条件．     

Bifurcations of limit cycles in a Z6-equivariant planar vector field of degree 5

A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ≥ (2k + 1)2 - 1 for the perturbed Hamiltonian systems.     

连续反馈联想记忆的吸引域和指数收敛速度的估计

利用一些实分析技巧和Liapunov方法,重新估计了连续反馈联想记忆模式的吸引域及其中每一点趋向记忆模式的指数收敛速度,得到一些新的结果,这些结果可用于连续反馈联想记忆网络的容错性能评价及其综合过程.     

平面自治系统的规范型与闭轨族周期的临界点

本文通过平面复自治系统的规范型研究实系统具有可线性化的中心和鞍点的条件,定义了k-阶广义细中心及其判定量,给出了计算判定量的递推公式,并对三次系统,讨论了周期的临界点分枝问题.