Center conditions and cyclicity for a family of cubic systems: computer algebra approach
Fercec, Brigita (University of Maribor(Slovenia).Center for Applied Mathematics and Theoretical Physics)
Mahdi, Adam (University of North Carolina at Charlotte. Mathematics Department)

Fecha:	2013
Resumen:	Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. To that end we overcome the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we also determine the number of limit cycles bifurcating from each component of the center variety.
Nota:	Agraïments: B. Fercec is supported by the Slovenian Research Agency; A.M. is partially supported by NIH-NIGMS grant 1P50GM094503-01A0. The authors thank Prof. Colin Christopher who suggested how to prove the second case of Theorem 6 as well as Prof. Valery Romanovsky and Prof. Douglas Shafer for fruitful discussions. Most of the paper was written when B.F. was visiting the Department of Mathematics at UNC-Charlotte. The authors are also grateful to the referees for their useful comments, which helped to improve the presentation of this work.
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Cyclicity ; Limit cycles ; Center-focus problem
Publicado en:	Mathematics and computers in simulation, Vol. 87 (2013) , p. 55-67, ISSN 0378-4754

DOI: 10.1016/j.matcom.2013.02.003
PMID: 24223469

Postprint 19 p, 311.7 KB

El registro aparece en las colecciones:
Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
Artículos > Artículos de investigación
Artículos > Artículos publicados