Limit cycles of a class of hybrid piecewise differential systems with a discontinuity line of L shape
Anacona Cabrera, Marly Tatiana (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
Anacona Erazo, Gerardo (Universidade Federal de Goiás. Instituto de Matemática e Estatística)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2026
Abstract:	In this work we study a class of discontinuous hybrid piecewise differential systems formed by two linear Hamiltonian systems that we named piecewise hybrid Hamiltonian systems. More precisely, we consider the differential systems with Hamiltonian functions H1(x, y) = a1x + a2y + a3x2 + a4xy + a5y2 + A, H2(x,y) = b1x + a2y + b3x2 + b4xy + b5y2 + B, if (x, y) ∈ Σ + if (x, y) ∈ Σ- with reset maps R1(x) = sx on x ≥ 0 and R2(y) = ry ony ≥ 0for0 < r,s < 1, and A, B are either zero, or one of them is a nonzero homogeneous polynomial of degree 3, Σ + = {(x, y) ∈ R2 : x ≥ 0 and y ≥ 0} and Σ- is the closure of R2 \Σ+. We provide an upper bound for the maximum number of limit cycles that these hybrid piecewise differential systems can exhibit. In other words, we solve the extension of the 16th Hilbert problem to this class of hybrid differential systems.
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 ; Hybrid piecewise differential systems
Published in:	Nonlinear Analysis: Real World Applications, Vol. 88 (April 2026) , art. 104492, ISSN 1468-1218

DOI: 10.1016/j.nonrwa.2025.104492

Available from: 2028-04-30 Postprint 9 p, 322.1 KB

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