Home > Articles > Published articles > On the limit cycles of the piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center |
Date: | 2022 |
Abstract: | While the limit cycles of the discontinuous piecewise differential systems formed by two linear differential systems separated by one straight line have been studied intensively, and up to now there are examples of these systems with at most 3 limit cycles. There are almost no works studying the limit cycles of the discontinuous piecewise differential systems formed by one linear differential system and a quadratic polynomial differential system separated by one straight line. In this paper using the averaging theory up to seven order we prove that the discontinuous piecewise differential systems formed by a linear focus or center and a quadratic weak focus or center separated by one straight line can have 8 limit cycles. More precisely, at every order of the averaging theory from order one to order seven we provide the maximum number of limit cycles that can be obtained using the averaging theory. |
Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 |
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: | Linear focus ; Linear center ; Quadratic weak focus ; Quadratic center ; Limit cycle ; Discontinuous piecewise differential system |
Published in: | Chaos, solitons and fractals, Vol. 160 (July 2022) , art. 112256, ISSN 0960-0779 |
Postprint 11 p, 300.1 KB |