Abstract: In the nonlinear dynamic system, analyzing the influence of the system parameters on the stability and the amplitude of vibration under instable condition of the system is an important work. In this paper, aiming at a common model of the nonlinear dynamic system, a method for analyzing the nonlinear behavior and the instability of the system is proposed. An example shows that this method is very effective.

Key words: vibration and wave, nonlinear, dynamic, stability, limit cycle

摘要： 在非线性动力学系统中，分析系统参数的变化对系统稳定性影响和在系统不稳定的情况下系统参数对振动幅值的影响是十分重要的两个方面。针对常见的非线性动力学模型，提出了一个利用特征根判别、规范形计算等方法对系统非线性特性和稳定性进行分析计算的方法。应用该方法进行计算分析的实例说明该方法十分有效。

关键词: 振动与波, 非线性, 动力学, 稳定性, 极限环