Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1) SN - (B)

Autor(es)

Artes, Joan C. ^[1] ; Mota, Marcos C. ^[2] ; Rezende, Alex C. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193 - Spain

^[2] Univ Sao Paulo, Inst Ciencia Matemat & Computacao, BR-13566590 Sao Carlos, SP - Brazil

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 31, n. 09 JUL 2021.
• Citações Web of Science: 0

Resumo

This paper presents a global study of the class QsnSN(11) of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite singularity and an infinite singularity. This class can be divided into two different families, namely, QsnSN(11)(A) phase portraits possessing a finite saddle-node as the only finite singularity and QsnSN(11)(B) phase portraits possessing a finite saddle-node and also a simple finite elemental singularity. Each one of these two families is given by a specific normal form. The study of family QsnSN(11)(A) was reported in {[}Artes et al., 2020b] where the authors obtained 36 topologically distinct phase portraits for systems in the closure <(QsnSN(11)(A))over bar>. In this paper, we provide the complete study of the geometry of family QsnSN(11)(B). This family which modulo the action of the affine group and time homotheties is three-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the three-dimensional real projective space. The respective bifurcation diagram yields 631 subsets with 226 topologically distinct phase portraits for systems in the closure <(QsnSN(11)(B))over bar> within the representatives of QsnSN(11)(B) given by a specific normal form. Some of these phase portraits are proven to have at least three limit cycles. (AU)

• Processo FAPESP: 18/21320-7 - Investigação de sistemas diferenciais quadráticos planares de codimensão dois
• Beneficiário: Alex Carlucci Rezende
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático