Firstly , based on matlab language programs , the chaotic vibration characteristic maps of duffing equation are drawn . the sensitivity of initial value in chaotic vibration is straightly described . the critical parameters of cycle to chaos is determined 利用matlab语言程序绘制了duffing振子典型的混沌振动特征图，利用可视化方法直观描述混沌振动的初值敏感性；探讨了利用混沌振动中的初值敏感性来判断从周期到混沌的临界参数，以及混沌吸引子的分数维随某一振动参数的变化规律。
Through the analysis of non - linear dynamics and studies of controlling chaos vibration for the gear driving system , we find that complex actions will be get following with the changing of parameters in this system . furthermore , we also find that the chaotic vibration can be controlled by using the torques loaded controller 通过对齿轮传动系统的非线性动力学的分析和混沌振动控制的研究，发现齿轮传动系统随系统参数改变会产生复杂的动力学行为，而且借助力矩加载控制器可以达到抑制齿轮传动系统的混沌振动的目的。
Based on above background , a elastic slider - crank mechanism , which is a typical engineering chaotic vibration system , and its dynamical response are selected and analyzed , in order to realize the combination of chaotic theory with engineering application and to serve latest theory as the guidance for structure design 本文选取了弹性曲柄滑块机构这一典型的工程混沌振动系统为研究对象，研究其动力学行为，以期将混沌振动理论研究与工程实用结合起来，使学科前沿的理论成果能对具体的弹性结构设计发挥指导作用。
