李雅普诺夫指数
摄动(天文学)
控制理论(社会学)
李雅普诺夫函数
数学
统计物理学
应用数学
物理
数学分析
计算机科学
非线性系统
人工智能
量子力学
控制(管理)
作者
Marek Balcerzak,Artur Dabrowski,Barbara Blazejczyk–Okolewska,Andrzej Stefanski
标识
DOI:10.1016/j.ymssp.2020.106734
摘要
Abstract This paper presents a novel, simple method of Lyapunov Exponents (LEs) spectrum estimation for non-smooth and discontinuous systems. The presented algorithm works for continuous-time dynamical systems, as well as for discrete maps. Its simplicity and flexibility enables to estimate LEs of complex, discontinuous systems in an easy manner. The paper starts with a comprehensive review of the state-of-art methods of the LEs computation for non-smooth systems. Then, the novel algorithm is introduced. Further on, examples of its use are provided. The presented applications include non-smooth and discontinuous maps, as well as continuous-time mechanical systems with discontinuities induced by impacts or by dry friction. The paper confirms that the method is simple, effective and robust. The presented algorithm can facilitate research in a large class of discontinuous systems, including stick-slip oscillators and many others.
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