Limit cycles of discontinuous piecewise hybrid rigid systems separated by a straight line
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Sánchez, Angela C. T. (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
Tonon, Durval José (Universidade Federal de Goiás. Instituto de Matemática e Estatística)

Date:	2026
Abstract:	A hybrid dynamical system is one whose behavior is governed by both continuous and discrete dynamics; that is, it exhibits both flows and jumps. The field of hybrid dynamical systems is relatively recent and encompasses a broad range of phenomena, and is often used to model various natural processes. In this paper, we investigate the maximum number of limit cycles that can arise in certain classes of discontinuous piecewise differential systems. These systems consist of two hybrid rigid subsystems separated by a straight line, where each rigid subsystem is composed of a linear center perturbed by a homogeneous polynomial of degree 2, 3, 4, 5 or 6. For these classes of piecewise systems, we address the extended 16th Hilbert problem.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Generalitat de Catalunya 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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 cycles ; Discontinuous piecewise differential systems ; Rigid systems ; Hybrid system
Published in:	Nonlinear Analysis: Real World Applications, Vol. 91 (October 2026) , art. 104607, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2026.104607

Available from: 2028-10-30 Postprint 19 p, 322.0 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