含参数的机械系统在阻尼优化问题中的稳定性与分岔分析

Stability and Bifurcation of Mechanical System with Parameters in Damping Optimization Problem

摘要: 本文讨论了含参数的机械系统在阻尼优化问题中的动力学行为。通过拟不可积的哈密顿理论来研究它的稳定性及Hopf分岔问题，再通过最大Lyapunov指数理论和边界种类来分析它的局部稳定性和全局稳定性。根据解决得到的FPK方程得到平稳概率密度函数和联合概率密度函数，进行数值模拟，最后说明参数变化对分岔的影响。

Abstract: The paper discusses the dynamical behavior of mechanical system containing parameter with damping optimization, and studies the stability and Hopf bifurcation of the system by using quasi- nonintegrable Hamilton system theory. Then, the conditions of local and global stability of system obtain the largest Lyapunov exponent boundary and category. Next, we solve stationary probability density function and jointly stationary probability density function by using FPK equation. Finally, we illustrate the result of bifurcation by parametric variation.