It is discovered in the rlc circuit model that type v intermittency becomes the main route of the transition from periodic motion to chaos . this type of intermittency can happen only in piecewise - smooth dissipative systems 在带模拟开关的rlc电路模型中发现v型阵发成为主要的从周期运动向混沌运动过渡的形式，这种阵发类型只能在分段光滑耗散系统中发生。
The last one is a new optimal control method based on krasovskii theory , which makes it possible to drive and change the state of a system easily and control the chaotic motions of a system effectively 第三就是在krasovskii理论的基础上提出了一种新的优化控制方法，这一方法使得我们可以根据实际需要随意改变系统状态，并能够以理想的效果将系统混沌运动控制到目标态上去。
Meanwhile , we analyze the procession of the route from the periodic motion to chaos motion of cable via period - doubling bifurcation . in chapter 5 , the chaotic motion of cable is studied by utilizing melnikov method and simulates the chaotic motion digitally 在第五章中，针对第四章得到的结论，用melnikov方法研究了斜拉索的混沌运动，并对斜拉索的混沌运动进行了数值模拟。
The results reveal that the addition of stochastic excitation can make the parameter threshold value for the rising of the chaotic motions vary in a wider region , and so , the chaotic motions will appear easily in the system 数值结果和理论结果吻合得很好，证明本文的推广是有效的。结果表明，适当的随机激励可以使得系统出现混沌运动的参数阈值变化范围更大，从而系统的混沌运动更容易出现。
In the present thesis , considering the impurity of the real material , we introduce the double - potential well and investigate that how the bottom fluctuation of the potential well influence the particle ' s chaos motion . my work includes the following points : 1 本文考虑到实际的材料中的杂质问题，而引入了双势阱，考察势阱底部的起伏对系统混沌运动的影响，主要进行了以下两个方面的工作： 1
Theories , numerical values and experiments indicates that chaos motion exists in all the fields of natural science ( even in sociology ) , which means that chaos motions is a motions of matter in nature and exists extensively in many non - linear systems 来自理论、数值计算和实验手段所揭示的自然科学(乃至社会科学)各个学科领域的许多系统中存在混沌运动的事实表明：混沌运动也是自然界物质运动的一种形式，而且它也广泛地存在于相当多的非线性系统中。
