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| Home > Articles > Published articles > Coexistence of Analytic and Piecewise Analytic Limit Cycles in Planar Piecewise Quadratic Differential Systems |
(Universidade Federal de São Carlos. Departamento de Matemática) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 2025 |
| Abstract: | We study the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. These limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the separation line. All the limit cycles are of small amplitude. This bifurcation creates a configuration of limit cycles of type (3,5,3). Additionally, in each half-plane, the maximum number of small-amplitude hyperbolic limit cycles that a quadratic vector field can have is three. |
| Grants: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Agencia Estatal de Investigación PID2022-136613NB-I00 Agencia Estatal de Investigación CEX2020-001084-M European Commission 777911 |
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| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Piecewise quadratic vector fields ; Limit cycles ; Simultaneous bifurcation ; Degenerate Hopf bifurcation |
| Published in: | Qualitative theory of dynamical systems, Vol. 24, Issue 2 (April 2025) , art. 103, ISSN 1662-3592 |
Postprint |
