| Full text | |
| Author(s): |
Braga, Denis de Carvalho
;
da Fonseca, Alexander Fernandes
;
Mello, Luis Fernando
;
Ribeiro, Ronisio Moises
;
Pessoa, Claudio Gomes
Total Authors: 5
|
| Document type: | Journal article |
| Source: | INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 33, n. 10, p. 17-pg., 2023-08-01. |
| Abstract | |
The main topic studied in this article is the number of crossing limit cycles bifurcating from two or three period annuli in discontinuous planar piecewise linear Hamiltonian differential systems with three zones. With regard to the studies already published in the literature on this subject, we highlight the following five aspects of our work: (1) the expressions of the first order Melnikov functions for suitable perturbations of a piecewise Hamiltonian system with three zones separated by two parallel lines are obtained explicitly; (2) the way the Melnikov functions are obtained is different from what has already been done for similar studies; (3) the expressions of the Melnikov functions are used to estimate the number of crossing limit cycles that bifurcate simultaneously from period annuli under suitable polynomial perturbations; (4) since the piecewise Hamiltonian system studied here has no symmetry, the number of crossing limit cycles bifurcating from the period annuli is greater than or equal to those obtained in systems already studied; (5) unlike other similar studies, we present a concrete example of a piecewise linear near-Hamiltonian differential system in which the lower bound of the number of limit cycles that bifurcate from the period annuli is reached. (AU) | |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 23/04061-6 - Continuous or piecewise smooth dynamical systems on 2 and 3 dimensional manifolds. |
| Grantee: | Cláudio Gomes Pessoa |
| Support Opportunities: | Regular Research Grants |