Center conditions and cyclicity for a family of cubic systems: computer algebra approach

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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)

Data:	2013
Resum:	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.
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Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Cyclicity ; Limit cycles ; Center-focus problem
Publicat a:	Mathematics and computers in simulation, Vol. 87 (2013) , p. 55-67, ISSN 0378-4754

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