dc.contributor.author
Coll, B.
dc.contributor.author
Gasull, A.
dc.contributor.author
Prohens, R.
dc.date.accessioned
2023-08-29T10:36:47Z
dc.date.accessioned
2024-09-19T14:35:39Z
dc.date.available
2023-08-29T10:36:47Z
dc.date.available
2024-09-19T14:35:39Z
dc.date.issued
2023-07-08
dc.identifier.uri
http://hdl.handle.net/2072/536861
dc.description.abstract
The goal of this work is the study of the probability of occurrence of limit cycles for a family of planar differential systems that are a natural extension of linear ones. To prove our results we first develop several results of non-existence, existence, uniqueness and non-uniqueness of limit cycles for this family. They are obtained by studying some Abelian integrals, via degenerate Andronov-Hopf bifurcations or by using the Bendixson-Dulac criterion. To the best of our knowledge, this is the first time that the probability of existence of limit cycles for a non-trivial family of planar systems is obtained analytically. In particular, we give vector fields for which the probability of having limit cycles is positive, but as small as desired. © 2023 The Author(s)
eng
dc.description.sponsorship
The first and third authors are partially supported by the Spanish and European Regional Development Funds (ERDF) Ministerio de Ciencia e Innovación ( PID2020-118726GB-I00 grant) The second author is partially supported by the Ministerio de Ciencia e Innovación ( PID2019-104658GB-I00 grant), by the grant Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D, Ministerio de Ciencia e Innovación ( CEX2020-001084-M grant) and also by the Agència de Gestió d'Ajuts Universitaris i de Recerca ( 2021 SGR 00113 grant).
dc.format.extent
24 p.
cat
dc.publisher
Elsevier (Academic Press Inc.)
cat
dc.relation.ispartof
Journal of Differential Equations
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Abelian integral; Degenetare Andronov-Hopf bifurcation; Limit cycle; Ordinary differential equations with random coefficients
cat
dc.title
Probability of existence of limit cycles for a family of planar systems
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1016/j.jde.2023.07.015
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
