一类扩张了的软弹簧型Duffing方程的紊动性态

本文用Melnikov函数方法讨论了一类扩张了的软弹簧型Duffing方程(k=1,2,3,…)在周期激励下的紊动现象.给出了出现二阶同宿切的条件.文中所采用的方法对于不能给出并宿轨道的显式的系统的研究是非常有用的.     

A group of chaotic motion of soft spring quadratic duffing equations

In this paper,we use the Melnikov function method to study a kind of soft Duffing equations(?) Af((?),x) x-x~(2k 1)=r[M(x,(?))cosωt N(x,(?))sinωt](k=1,2,3…)and give the condition that the equations have chaotic motion and bifurcation.The method used in this paper is effective for dealing with the Melnikov function integral of the system whose explict expression of the homoclinic or heteroclinic orbit cannot be given.     

软弹簧型Duffing方程在摄动下分支出的极限环

在这篇文章中,作者用Melnikov函数方法分析了软弹簧型Duffing方程[1]在摄动下异宿轨道破裂后稳定流形与不稳定流形的相对位置,给出了方程在不同摄动下分支出极限环的条件与极限环的位置.     

Limit circles bifurcated from a soft spring duffing equation under perturbation

I.IntroductionThesoft'springDuffingEquationhasbeenextensivelyappliedinelectricsandmechanics.Foralongtime,scientistshavedonemanyresearchforit.IntheRef.[11,thereisadetaileddiscussiononChaosandSubharmonicorbitscausedbyperiodicperturbation.111thissection,weconcentrateontheequationofamassonasoftspringanddiscussitsbasiccharacteristics.Intheequation(l.l),177expressesthemass,CandNrespectivel}'expressesdolinearandnonlinearspringcoefficients,DisafunctionD(X)aboutthephaseX.SettingX=x~,T=Dot,ado=~,…     

一类推扩的 Holmes 型 Duffing 方程的紊动性态

Duffing 方程在力学、电学及物理学中都有广泛的应用,许多科学工作者做过大量的工作,这类方程在周期激励下的紊动现象的研究是近几年才开始的.[1]对 Moon 和Holmes 修改了的 Duffing 方程的紊动性态有较详细的概述.本文对推广了的 Holmes型 Duffing 方程