单自由度碰振系统的Lyapunov指数分析

Analysis of the Lyapunov Exponent in A Degree of Freedom Vibro-impact System

该文考虑了单自由度振子的碰振运动,直接给出振子发生擦边余维二分岔的条件,通过数值模拟,给出了不同参数下系统在擦边余维二分岔点附近区域的相图,并计算相应的Lyapunov指数.验算结果表明系统经历擦边余维二分岔进入混沌.

A single-degree-of-freedom oscillator of the impact motion is investigated.And the condition that the system must satisfy for co-dimension-two grazing bifurcation to occur is given directly.The phase diagrams of the system near the points of co-dimension-two grazing bifurcation with different parameters are given via the numerical simulation,at the same time the corresponding Lyapunov exponents are calculated.It shows that the system enters chaos due to the co-dimension-two grazing bifurcation.