Determining Lyapunov exponents of non-smooth systems: Perturbation vectors approach
| Autor: | Artur Dabrowski, Barbara Blazejczyk–Okolewska, Andrzej Stefanski, Marek Balcerzak |
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| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Dynamical systems theory Computer science Mechanical Engineering Computation Aerospace Engineering Perturbation (astronomy) 02 engineering and technology Lyapunov exponent Classification of discontinuities Discontinuous systems Non smooth 01 natural sciences Computer Science Applications Mechanical system symbols.namesake 020901 industrial engineering & automation Control and Systems Engineering 0103 physical sciences Signal Processing symbols Applied mathematics 010301 acoustics ComputingMethodologies_COMPUTERGRAPHICS Civil and Structural Engineering |
| Zdroj: | Mechanical Systems and Signal Processing. 141:106734 |
| ISSN: | 0888-3270 |
| DOI: | 10.1016/j.ymssp.2020.106734 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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