The number of limit cycles for a family of polynomial systems |
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Authors: | Guanghui Xiang Maoan Han Tonghua Zhang |
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Affiliation: | Department of Mathematics, Shanghai Jiao Tong University Shanghai 200240, P.R. China |
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Abstract: | In this paper, the number of limit cycles in a family of polynomial systems was studied by the bifurcation methods. With the help of a computer algebra system (e.g., Maple 7.0), we obtain that the least upper bound for the number of limit cycles appearing in a global bifurcation of systems (2.1) and (2.2) is 5n + 5 + (1 − (−1)n)/2 for c ≠ 0 and n for c ≡ 0. |
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Keywords: | Hilbert's 16th problem Global bifurcation Abelian integrals Limit cycles |
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