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Estimating the number of limit cycles in polynomials systems |
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| Authors: | Maoan Han |
| Institution: | a Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China b CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia c Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia |
| Abstract: | We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limit cycles can bifurcate from any center or focus at the origin of the system. |
| Keywords: | Limit cycles Bifurcations Cyclicity |
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