Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1, 1) SN-(B)
This paper presents a global study of the class QsnSN11 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 d...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:303178 |
| Acceso en línea: | https://ddd.uab.cat/record/303178 https://dx.doi.org/urn:doi:10.1142/S0218127421300263 |
| Access Level: | acceso abierto |
| Palabra clave: | Quadratic differential system Finite saddle-node Finite elemental singularity Infinite saddle-node Phase portrait Bifurcation diagram Algebraic invariant |
| Sumario: | This paper presents a global study of the class QsnSN11 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, QsnSN11(A) phase portraits possessing a finite saddle-node as the only finite singularity and QsnSN11(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 QsnSN11(A) was reported in [Artés et al., 2020b] where the authors obtained 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯. In this paper, we provide the complete study of the geometry of family QsnSN11(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 QsnSN11(B)¯ within the representatives of QsnSN11(B) given by a specific normal form. Some of these phase portraits are proven to have at least three limit cycles. |
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