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

Joan Carles Artés Ferragud; Marcos C. Mota; Alex C. Rezende

doi:10.1142/S0218127421500267

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

Joan Carles Artés Ferragud, Marcos C. Mota, Alex C. Rezende

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

8 Cites (Scopus)

Resum

Our goal is to make 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 and infinite singularities. This class can be divided into two different families, being (A) possessing the finite saddle-node as the only finite singularity and (B) possessing the finite saddle-node and also a finite simple elemental singularity. In this paper we provide the complete study of the geometry of family (A). The family (A) modulo the action of the affine group and time homotheties are four-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the four-dimensional real projective space ℝℙ4. As far as we know, this is the first time that a complete family is studied in the four-dimensional real projective space. The respective bifurcation diagram yields 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯ within the representatives of QsnSN11(A) given by a specific normal form.

Idioma original	Anglès
Revista	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volum	31
Número	2
DOIs	https://doi.org/10.1142/S0218127421500267
Estat de la publicació	En premsa - 2021

Accés al document

10.1142/S0218127421500267

https://ddd.uab.cat/record/303175

Algunos aspectos de la dinámica local y global de los sistemas dinámicos contínuos y discretos: Integrabilidad, Periodicidad y Bifurcaciones
Llibre Salo, J. (PI), Torregrosa i Arús, J. (Investigador/a Principal 2), Buzzi, C. A. (Col.laborador/a), Candido , M. R. (Col.laborador/a), Carvalho, Y. R. (Col.laborador/a), Caubergh , M. M. (Col.laborador/a), Cornelio, J. L. (Col.laborador/a), Cousillas, G. (Col.laborador/a), Cufi Cabre, C. (Col.laborador/a), Diz Pita, É. (Col.laborador/a), Ferragut Amengual, A. M. (Col.laborador/a), Ferragut Amengual, A. (Col.laborador/a), Geyer, A. (Col.laborador/a), Giacomini, H. J. (Col.laborador/a), Gouveia, L. F. (Col.laborador/a), Jiménez Ruíz, J. J. (Col.laborador/a), Lembarki, F. (Col.laborador/a), Martínez, Y. P. (Col.laborador/a), Pérez González, S. (Col.laborador/a), Ramírez, V. (Col.laborador/a), Saleta Reig, O. (Col.laborador/a), Sanchez Sanchez, I. (Col.laborador/a), Santos, R. A. T. (Col.laborador/a), Schlomiuk, D. (Col.laborador/a), Valls Angles, C. (Col.laborador/a), Vulpe, N. (Col.laborador/a), Zhang, X. (Col.laborador/a), da Cruz, L. P. C. (Col.laborador/a), de Almedia Silva Menezes, L. (Col.laborador/a), Artes Ferragud, J. C. (Investigador/a), Caubergh , M. M. (Investigador/a), Cima Mollet, A. M. (Investigador/a), Corbera Subirana, M. (Investigador/a), Cors Iglesias, J. M. (Investigador/a), Gasull Embid, A. (Investigador/a), Pantazi, C. (Investigador/a) & Soler Villanueva, J. (Investigador/a)
Ministerio de Economía y Competitividad (MINECO)
30/12/16 → 31/12/20
Projecte: Projectes i Ajuts a la Recerca

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@article{ce48ab9f02b9451b95acdbc2e26960a6,

title = "Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1) SN - (A)",

abstract = "Our goal is to make 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 and infinite singularities. This class can be divided into two different families, being (A) possessing the finite saddle-node as the only finite singularity and (B) possessing the finite saddle-node and also a finite simple elemental singularity. In this paper we provide the complete study of the geometry of family (A). The family (A) modulo the action of the affine group and time homotheties are four-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the four-dimensional real projective space ℝℙ4. As far as we know, this is the first time that a complete family is studied in the four-dimensional real projective space. The respective bifurcation diagram yields 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯ within the representatives of QsnSN11(A) given by a specific normal form.",

keywords = "Quadratic differential system, Finite saddle-node, Infinite saddle-node, Phase portrait, Bifurcation diagram, Algebraic invariant",

author = "{Art{\'e}s Ferragud}, {Joan Carles} and Mota, {Marcos C.} and Rezende, {Alex C.}",

year = "2021",

doi = "10.1142/S0218127421500267",

language = "English",

volume = "31",

number = "2",

}

Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1) SN - (A). / Artés Ferragud, Joan Carles; Mota, Marcos C.; Rezende, Alex C.
In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 31, Núm. 2, 2021.

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

TY - JOUR

T1 - Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1) SN - (A)

AU - Artés Ferragud, Joan Carles

AU - Mota, Marcos C.

AU - Rezende, Alex C.

PY - 2021

Y1 - 2021

N2 - Our goal is to make 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 and infinite singularities. This class can be divided into two different families, being (A) possessing the finite saddle-node as the only finite singularity and (B) possessing the finite saddle-node and also a finite simple elemental singularity. In this paper we provide the complete study of the geometry of family (A). The family (A) modulo the action of the affine group and time homotheties are four-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the four-dimensional real projective space ℝℙ4. As far as we know, this is the first time that a complete family is studied in the four-dimensional real projective space. The respective bifurcation diagram yields 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯ within the representatives of QsnSN11(A) given by a specific normal form.

AB - Our goal is to make 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 and infinite singularities. This class can be divided into two different families, being (A) possessing the finite saddle-node as the only finite singularity and (B) possessing the finite saddle-node and also a finite simple elemental singularity. In this paper we provide the complete study of the geometry of family (A). The family (A) modulo the action of the affine group and time homotheties are four-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the four-dimensional real projective space ℝℙ4. As far as we know, this is the first time that a complete family is studied in the four-dimensional real projective space. The respective bifurcation diagram yields 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯ within the representatives of QsnSN11(A) given by a specific normal form.

KW - Quadratic differential system

KW - Finite saddle-node

KW - Infinite saddle-node

KW - Phase portrait

KW - Bifurcation diagram

KW - Algebraic invariant

U2 - 10.1142/S0218127421500267

DO - 10.1142/S0218127421500267

M3 - Article

SN - 0218-1274

VL - 31

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 2

ER -

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

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Algunos aspectos de la dinámica local y global de los sistemas dinámicos contínuos y discretos: Integrabilidad, Periodicidad y Bifurcaciones

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