Szczegóły publikacji
Opis bibliograficzny
Symbolic dynamics approach to find periodic windows: the case study of the Rössler system / Zbigniew GALIAS // Communications in Nonlinear Science and Numerical Simulation ; ISSN 1007-5704. — 2025 — vol. 140 pt. 1 art. no. 108403, s. 1–12. — Bibliogr. s. 11–12, Abstr. — Publikacja dostępna online od: 2024-10-24
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 156815 |
|---|---|
| Data dodania do BaDAP | 2025-01-10 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.cnsns.2024.108403 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Communications in Nonlinear Science & Numerical Simulation |
Abstract
Modification of a parameter of a chaotic system may lead to the emergence of a periodic attractor. Under certain assumptions periodic windows (regions in the parameter space in which a periodic attractor exists) densely fill a chaotic region. Usually it is very difficult to prove this property. In this work, we propose a systematic procedure to locate and prove the existence of periodic windows. The method combines the symbolic dynamics based approach to find unstable periodic orbits (UPOs), the continuation method to locate periodic windows (PWs), and interval arithmetic tools to prove their existence. The proposed method is applied to the R & ouml;ssler system. The existence of several thousands of PWs close to the classical parameter values is proved and periodic attractors very close in the parameter space to the classical R & ouml;ssler attractor are found. Estimates of measures of sets of parameters for which a periodic attractor exists are calculated.
