Limit cycles of discontinuous piecewise polynomial vector fields

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• 作者：Tiago de Carvalho^a ; ^{tcarvalho@fc.unesp.br} ; Jaume Llibre^b ; ^{jllibre@mat.uab.cat} ; Durval Jos&eacute ; Tonon^c ; ^{djtonon@ufg.br}
• 关键词：Piecewise smooth vector fields ; Limit cycle ; Averaging theory ; Cyclicity
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：572-579
• 全文大小：311 K
• 卷排序：449

文摘

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.