Homoclinic bifurcation in a quasiperiodically excited impact inverted pendulum

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• 作者：Junming Gao (1)
  Zhengdong Du (1)
  
  1. Department of Mathematics ; Sichuan University ; Chengdu ; 610064 ; Sichuan ; People鈥檚 Republic of China
  
• 关键词：Impact oscillator ; Quasiperiodic excitation ; Melnikov method ; Homoclinic bifurcation ; Chaos ; 34C15 ; 34G25 ; 37C29
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：79
• 期：2
• 页码：1061-1074
• 全文大小：3,542 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

Homoclinic bifurcation for a nonlinear inverted pendulum impacting between two rigid walls under external quasiperiodic excitation is analyzed. The results for the homoclinic bifurcation of quasiperiodically excited smooth systems obtained by Ide and Wiggins are extended to the non-smooth ones. We present a method of Melnikov type to derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally. Such a transversal Intersection implies the appearance of Smale horseshoe-type chaotic dynamics that is similar to that in the periodically forced smooth systems. As an application, by using a combination of analytical and numerical methods, a quasiperiodically excited impact oscillator of Duffing type with two frequencies is studied in detail.