Determining Lyapunov exponents of non-smooth systems: Perturbation vectors approach

被引：42

作者：

Balcerzak, Marek ^{[1
]}

Dabrowski, Artur ^{[1
]}

Blazejczyk-Okolewska, Barbara ^{[1
]}

Stefanski, Andrzej ^{[1
]}

机构：

[1] Lodz Univ Technol, Div Dynam, Stefanowskiego 1-15, Lodz, Poland

来源：

MECHANICAL SYSTEMS AND SIGNAL PROCESSING | 2020年 / 141卷

关键词：

Lyapunov exponents; Perturbation methods; Non-smooth systems; Discontinuous systems; Stick-slip; MAPS; BIFURCATIONS; CHAOS;

D O I：

10.1016/j.ymssp.2020.106734

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

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. (C) 2020 The Authors. Published by Elsevier Ltd.

引用

页数：24

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