非光滑系统全局动力学Melnikov方法的研究进展  

RESEARCH PROGRESS IN MELNIKOV METHOD FOR GLOBAL DYNAMICS OF NON-SMOOTH SYSTEMS

作　　者：李双宝[1] 马茜茜 张伟[2] Li Shuangbao;Ma Xixi;Zhang Wei(Civil Aviation University of China,Tianjin 300300,China;College of Mechanical Engineering,Beijing University of Technology,Beijing 100022,China)

机构地区：[1]中国民航大学理学院,天津300300 [2]北京工业大学机电学院,北京100124

出　　处：《动力学与控制学报》2020年第2期9-20,共12页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11672326)。

摘　　要：近年来,非光滑系统的全局动力学问题引起了国内外学者的广泛关注.由于系统的非光滑性,使得经典的Melnikov方法在非光滑系统全局动力学的研究中不再适用,因此,推广非光滑系统全局分岔和混沌动力学的Melnikov方法是近年来非光滑系统研究的一个难点和热点问题.本文对近年来在此领域的研究进展进行了全面的综述比较,特别地考虑解析方法应具有几何直观性和工程计算方面的优势,介绍了本文作者近几年来发展非光滑系统全局动力学Melnikov方法的研究工作.In recent years,the global dynamics of non-smooth systems has aroused widespread concern both at home and abroad.Due to the non-smoothness of the system,the classical Melnikov method is no longer applicable to studying the global dynamics.Therefore,extending the Melnikov method to the non-smooth systems for global bifurcation and chaotic dynamics is still a difficult but hot topic.In this paper,a comprehensive review on the research progress in this field in recent years was given,especially those works on the analytical methods having advantages of geometry intuitiveness and engineering calculations.The research works by the authors on developing the Melnikov method for global dynamics of non-smooth systems were also summarized.

关 键 词：非光滑系统 开关流形 同宿轨道 MELNIKOV方法 碰撞映射 

分 类 号：O175[理学—数学]