2026-07-10T08:39:07Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/407272021-06-24T07:41:23Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
Uniqueness of limit cycles for quadratic vector fields
Bravo, José Luis
Fernández, Manuel
Ojeda, Ignacio
Sánchez, Fernándo
Abel equation
Ecuación de Abel
Closed solution
Solución en forma cerrada
Periodic solution
Solución periódica
Limit cycles
Ciclos límite
Producción Científica
This article deals with the study of the number of limit
cycles surrounding a critical point of a quadratic planar vector field,
which, in normal form, can be written as x
′ = a1x − y − a3x
2 + (2a2 +
a5)xy+a6y
2
, y
′ = x+a1y+a2x
2+(2a3+a4)xy−a2y
2
. In particular, we
study the semi-varieties defined in terms of the parameters a1, a2, . . . , a6
where some classical criteria for the associated Abel equation apply.
The proofs will combine classical ideas with tools from computational
algebraic geometry.
Agencia Estatal de Investigación - Fondo Europeo de Desarrollo Regional (grant MTM 2011-22751)
Junta de Extremadura (grant GR15055)
Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-65764-C3-1-P)
2020-04-06T19:33:18Z
2020-04-06T19:33:18Z
2019
info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
Discrete and Continuous Dynamical Systems, 2019, vol. 39, n. 1. p. 483-502
1553-5231
http://uvadoc.uva.es/handle/10324/40727
10.3934/dcds.2019020
eng
http://www.aimsciences.org/article/doi/10.3934/dcds.2019020
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/
© 2019 American Institute of Mathematical Sciences
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American Institute of Mathematical Sciences
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UVaDOC. Repositorio Documental de la Universidad de Valladolid
http://uvadoc.uva.es/handle/10324/40727