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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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Cyclicity ; Limit cycles ; Center-focus problem
Publicat a: Mathematics and Computers in Simulation, Vol. 87 (2013) , p. 55-67, ISSN 0378-4754

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

19 p, 311.7 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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