期刊导航

论文摘要

倒置单摆在拟周期扰动下的同宿分岔

Homoclinic bifurcation in quasiperiodically forced inverted pendulum

作者:高俊明(四川大学数学学院)

Author:GAO Jun-Ming(College of Mathematics, Sichuan University)

收稿日期:2013-12-18          年卷(期)页码:2015,52(1):11-15

期刊名称:四川大学学报: 自然科学版

Journal Name:Journal of Sichuan University (Natural Science Edition)

关键字:分段光滑动力系统; 拟周期扰动; Melnikov方法; 同宿分岔

Key words:Piecewise smooth system; Quasiperiodic excitation; Melnikov method; Homoclinic bifurcation

基金项目:中央高校基本科研业务费专项基金资助(2010SCU21005)

中文摘要

为讨论一类具有双侧刚性约束的非线性倒置单摆的同宿轨在含有两个基本频率的拟周期外力扰动下的分岔, 本文将原本适用于光滑系统的Melnikov方法推广到了此类系统并导出了相应的Melnikov函数的计算公式, 由此给出了扰动系统稳定流形与不稳定流形横截相交的一个充分条件.

英文摘要

We discuss the homoclinic bifurcation for a nonlinear inverted pendulum impacting between two rigid walls under external quasiperiodic excitation with two fundamental frequencies. The Melnikov method established for smooth dynamical systems is extended to be applicable to the general quasiperiodic excited impact system. We present a method to compute the first order Melnikov function to derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally.

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