Transformations of Closed Invariant Curves and Closed-Invariant-Curve-Like Chaotic Attractors in Piecewise Smooth Systems

Autor:	Viktor Avrutin, Frank Bastian, Zhanybai T. Zhusubaliyev
Rok vydání:	2021
Předmět:	Nonlinear Sciences::Chaotic Dynamics Quasiperiodicity Phase portrait Applied Mathematics Modeling and Simulation Attractor Mathematical analysis Chaotic Piecewise Invariant (mathematics) Engineering (miscellaneous) Mathematics
Zdroj:	International Journal of Bifurcation and Chaos. 31:2130009
ISSN:	1793-6551 0218-1274
DOI:	10.1142/s0218127421300093
Popis:	The paper describes some aspects of sudden transformations of closed invariant curves in a 2D piecewise smooth map. In particular, using detailed numerically calculated phase portraits, we discuss transitions from smooth to piecewise smooth closed invariant curves. We show that such transitions may occur not only when a closed invariant curve collides with a border but also via a homoclinic bifurcation. Furthermore, we describe an unusual transformation from a closed invariant curve to a large amplitude chaotic attractor and demonstrate that this transition occurs in two steps, involving a small amplitude closed-invariant-curve-like chaotic attractor.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0d81702f8c335afd0b3480a36d063f1b https://doi.org/10.1142/s0218127421300093 Zobrazit plný text záznamu