Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II)
He, Dongping (Sichuan University)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	In our previous work, we have studied the limit cycles for a class of discontinuous piecewise quadratic polynomial differential systems with a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle α=π/2. The unperturbed system is the quadratic uniform isochronous center x˙=-y+xy, y˙=x+y2 with a family of periodic orbits surrounding the origin. In this paper, we continue to investigate this kind of piecewise differential systems, but now the angle between the two rays is α∈(0,π/2)∪[3π/2,2π). Using the Chebyshev theory, we prove that the maximum number of hyperbolic limit cycles that can bifurcate from these periodic orbits using the averaging theory of first order is exactly 8 for α∈(0,π/2)∪[3π/2,2π). Together with our previous work, which concerns on the case of α=π/2, we can conclude that using the averaging theory of first order the maximum number of hyperbolic limit cycles is exactly 8, when this quadratic center is perturbed inside the above-mentioned classes separated by a non-regular line of discontinuity with α∈(0,π/2]∪[3π/2,2π).
Grants:	Agencia Estatal de Investigación PID2022-136613NB-100 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Acadèmia de Ciències i Arts de Barcelona
Rights:	Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Discontinuous piecewise polynomial system ; Quadratic uniform isochronous center ; Non-regular line of discontinuity ; Averaging theory ; Chebyshev theory
Published in:	Mediterranean journal of mathematics, Vol. 21, Issue 6 (September 2024) , art. 174, ISSN 1660-5454
Related work:	He, D., Llibre, J. Correction to: Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II). Mediterr. J. Math. 21, 192 (2024) https://doi.org/10.1007/s00009-024-02730-0

Correcció de l'article: https://ddd.uab.cat/record/307744
DOI: 10.1007/s00009-024-02714-0

Postprint 23 p, 413.0 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles