Fast and simple Lyapunov Exponents estimation in discontinuous systems
| Autor: | Artur Dabrowski, Tomasz Sagan, Marek Balcerzak, Andrzej Stefanski |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Dynamical systems theory
Computer science Computer Science::Information Retrieval media_common.quotation_subject Spectrum (functional analysis) General Physics and Astronomy Lyapunov exponent Discontinuous systems Field (computer science) symbols.namesake Simple (abstract algebra) symbols Applied mathematics General Materials Science Simplicity Physical and Theoretical Chemistry media_common |
| Zdroj: | The European Physical Journal Special Topics. 229:2167-2181 |
| ISSN: | 1951-6401 1951-6355 |
| DOI: | 10.1140/epjst/e2020-900275-x |
| Popis: | Typically, to estimate the whole spectrum ofnLyapunov Exponents (LEs), it is necessary to integratenperturbations and to orthogonalize them. Recently it has been shown that complexity of calculations can be reduced for smooth systems: integration of (n-1) perturbations is sufficient. In this paper authors demonstrate how this simplified approach can be adopted to non-smooth or discontinuous systems. Apart from the reduced complexity, the assets of the presented approach are simplicity and ease of implementation. The paper starts with a short review of properties of LEs and methods of their estimation for smooth and non-smooth systems. Then, the algorithm of reduced complexity for smooth systems is shortly introduced. Its adaptation to non-smooth systems is described in details. Application of the method is presented for an impact oscillator. Implementation of the novel algorithm is comprehensively explained. Results of simulations are presented and validated. It is expected that the presented method can simplify investigations of non-smooth dynamical systems and support research in this field. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink