| dc.contributor.author |
Giacomini, Héctor |
| dc.contributor.author |
Grau Montaña, Maite |
| dc.date |
2016-02-03T11:55:42Z |
| dc.date |
2017-03-01T01:02:56Z |
| dc.date |
2015 |
| dc.date |
2016-02-03T10:05:51Z |
| dc.identifier |
0022-247X |
| dc.identifier |
http://hdl.handle.net/10459.1/49434 |
| dc.identifier |
https://doi.org/10.1016/j.jmaa.2015.03.015 |
| dc.identifier.uri |
http://hdl.handle.net/10459.1/49434 |
| dc.description |
This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal conics. We present several examples of known systems in the literature showing diferent features about limit cycles: hyperbolicity, Hopf bifurcation, sky-blue bifurcation, rotated vector fields, . . . for which the obtained Poincaré-Bendixson region allows to locate the limit cycles. Our method gives bounds for the bifurcation values of parametrical families of planar vector fields and intervals of existence of limit cycles. |
| dc.description |
The authors are partially supported by MINECO/FEDER grant number MTM2011-22877 and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204 |
| dc.format |
application/pdf |
| dc.language |
eng |
| dc.publisher |
Elsevier |
| dc.relation |
MICINN/PN2008-2011/MTM2011-22877 |
| dc.relation |
Versió postprint del document publicat a https://doi.org/10.1016/j.jmaa.2015.03.015 |
| dc.relation |
Journal of Mathematical Analysis and Applications, 2015, vol. 428, p. 563-586 |
| dc.rights |
cc-by-nc-nd (c) Elsevier, 2015 |
| dc.rights |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights |
info:eu-repo/semantics/openAccess |
| dc.subject |
Transversal conic |
| dc.subject |
Poincaré–Bendixson region |
| dc.subject |
Limit cycle |
| dc.subject |
Planar differential system |
| dc.title |
Transversal conics and the existence of limit cycles |
| dc.type |
article |
| dc.type |
acceptedVersion |
