Limit cycle bifurcations from a non-degenerate center

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• 作者：Jaume Giné ; ^{gine@matematica.udl.cat}
• 关键词：Poincaré ; &ndash ; Liapunov constants ; Limit cycles ; Center problem ; Groebner basis
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 出版时间：1 January, 2012
• 年：2012
• 卷：218
• 期：9
• 页码：4703-4709
• 全文大小：192 K

文摘

In this work we discuss the computational problems which appear in the computation of the Poincar¨¦-Liapunov constants and the determination of their functionally independent number. Moreover, we calculate the minimum number of Bautin ideal generators which give the number of small limit cycles under certain hypothesis about the generators. In particular, we consider polynomial systems of the form , where P_n and Q_n are a homogeneous polynomial of degree n. We use center bifurcation rather than multiple Hopf bifurcations, used a previous work , to estimate the cyclicity of a unique singular point of focus-center type for n = 4, 5, 6, 7 and compare with the results given by the conjecture presented in .