强非对称恢复力振子的极限环分析与计算

Analysis and Calculation of Limit Cycles for Oscillator with Strongly Non-Symmetrical Restoring Force

本文利用中的渐近分析方法,研究了具有强非对称恢复力振子的极限环,即:d^2x/dt^2+ε(H_0+H_2x_2)dx/dt+M_1x+M_2x^2+M_3x^3=0_3得到几种情形下的极限环幅值的计算公式,讨论了强非对称恢复力对极限环的影响,并得到极限环内部包含两个奇点(其中之一必为高次奇点)的特征,最后给出理论分析结果与数值计算结果的比较,证实分析结果的正确性。

In this paper, limit cycles of occillator with strongly mon-symmetrical restoring force are investigated by means of the method of asymptotic analysis in thepaper, i. e., d^2x/dt_2+ε(H_0+H_2x^2)dx/dt+M_1x+M_2x^2+M_3x^3=0. Calculating formulae of limit cycles are presented for several cases. Influence of strongly non-symmetrical restoring force on limit cycles is discussed, and a feature of two singular points in one limit cycle is obtained. Finally theoretical results are compared to numerical reults, which shows that the analysis results in this paper are reliable.