Limit cycles in a class of planar discontinuous piecewise quadratic differential systems with a non-regular line of discontinuity (I)
He, Dongping (Sichuan University. School of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2025
Abstract:	In this paper we study the limit cycles which bifurcate from the periodic orbits of the quadratic uniform isochronous center ẋ = -y + xy, ẏ = x + y, when this center is perturbed inside the class of all discontinuous piecewise quadratic polynomial differential systems in the plane with two pieces separated by a non-regular line of discontinuity, which is formed by two rays starting from the origin and forming an angle α = π/2. Using the Chebyshev theory we prove that the maximum number of hyperbolic limit cycles which can bifurcate from these periodic orbits is exactly 8 using the averaging theory of first order. For this class of discontinuous piecewise differential systems we obtain three more limit cycles than the line of discontinuity is regular, i. e. , the case of where the two rays form an angle α = π.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Discontinuous piecewise polynomial system ; Quadratic uniform isochronous center ; Non-regular discontinuous boundary ; Averaging theory ; Chebyshev theory
Published in:	Mathematics and computers in simulation, Vol. 229 (March 2025) , p. 743-757, ISSN 0378-4754

DOI: 10.1016/j.matcom.2024.10.016

Available from: 2027-03-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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