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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Artes, Joan C. [1] ; Mota, Marcos C. [2] ; Rezende, Alex C. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 31, n. 09 JUL 2021.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 18/21320-7 - Investigation of planar quadratic differential systems of codimension two
Grantee:Alex Carlucci Rezende
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 19/21181-0 - New frontiers in Singularity Theory
Grantee:Regilene Delazari dos Santos Oliveira
Support Opportunities: Research Projects - Thematic Grants