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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (1): 1-10.doi: https://doi.org/10.1007/s10483-011-1388-x

• Articles •    下一篇

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

刘延彬 陈予恕 曹庆杰   

  1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • 收稿日期:2010-07-20 修回日期:2010-11-09 出版日期:2011-01-10 发布日期:2011-01-01

Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters

 LIU Yan-Bin, CHEN Yu-Shu, CAO Qing-Jie   

  1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. R. China
  • Received:2010-07-20 Revised:2010-11-09 Online:2011-01-10 Published:2011-01-01

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摘要： The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.

Abstract: The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.

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