一类非线性动力系统的行为分析

The Behavior Analysis of a Class of Nonlinear Dynamic Systems

文章对一类经典的非线性动力系统模型——三级电子管电路的VAN DER POL方程进行稳定性分析.首先,通过线性近似法对该微分方程在零点处的稳定性态做出判断,得出结论:该方程在零点处不稳定.再证明该模型存在唯一的极限环,最后用二变量多尺度法求出该方程的周期解.通过所求得的周期解,近似得出该模型的极限环.

The articile makes the stability analysis of a class of the classic model of nonlinear dynamic systems-VAN DER POL equation which exists in the three tube circuit. First, through the linear approximation, we estimate the stability of the differential equation in zero. We conclude that this equation is instable in zero. Next, we prove that this model exists exclusive limit cycle. Last, using the method of two-variable multi-scale, we obtain the periodic solution and the limit cycle of this model.