含二次非线性项的受迫振子在主共振曲线上表现的浑沌特性

Chaotic Behavior of Forced Oscillator Containing a Square Nonlinear Term on Principal Resonance Curves

本文在［１］的基础上，用多尺度法和数值模拟对含二次非线性项的受迫振子作了进一步研究，探讨了其浑沌域与主共振曲线的关系，通过对主共振曲线稳定性的分析，我们推测浑沌运动将发生在主共振曲线具有垂直切线的频率附近，数值模拟结果证实了这一推测。这就为那些难以用Ｍｅｌｎｉｋｏｖ方法处理的系统，提供了一条寻求浑沌运动的可行途径。

Based on[1], we investigate the route to chaos in forced oscillator containing a square nonlinear term on principal resonance curves. And chaotic motion is observed against the background of classical resonance curves, stability limits and jump phenomena. It is shown that chaotic motion appears in the neighbourhood of the point both meeting condition that Molnikov function has simple zero and having the point of vertical tangent of the resonance curves.