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

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  • Ferčec, Brigita
  • Mahdi, Adam

Abstract

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.

Suggested Citation

  • Ferčec, Brigita & Mahdi, Adam, 2013. "Center conditions and cyclicity for a family of cubic systems: Computer algebra approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 55-67.
    • Handle: RePEc:eee:matcom:v:87:y:2013:i:c:p:55-67
    DOI: 10.1016/j.matcom.2013.02.003
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    References listed on IDEAS

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    1. Unknown, 2008. "Research Areas," Amber Waves:The Economics of Food, Farming, Natural Resources, and Rural America, United States Department of Agriculture, Economic Research Service, pages 1-3, February.
    2. Unknown, 2008. "Research Areas," Amber Waves:The Economics of Food, Farming, Natural Resources, and Rural America, United States Department of Agriculture, Economic Research Service, pages 1-3, September.
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    Cited by:

    1. Mencinger, Matej & Ferčec, Brigita, 2017. "The center and cyclicity problems for some analytic maps," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 73-85.
    2. Mencinger, Matej & Ferčec, Brigita & Oliveira, Regilene & Pagon, Dušan, 2017. "Cyclicity of some analytic maps," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 114-125.

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