Bounding the number of limit cycles for a polynomial Liénard system by using regular chains

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• 作者：Xianbo Sun^a ; ^{xianbo01@126.com" class="auth_mail" title="E-mail the corresponding author} ; Wentao Huang^b ; ^c ; ^{huangwentao@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Regular chain ; Limit cycle ; Lié ; nard system ; Melnikov function
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P2
• 页码：197-210
• 全文大小：374 K

文摘

In this paper, we study the bound of the number of limit cycles by Poincaré bifurcation for a Liénard system of type (4,3)$(4,3)$. An automatic algorithm is constructed based on the Chebyshev criteria and the tools of regular chain theory in polynomial algebra. We prove the system can bifurcate at most 6 limit cycles from the periodic annulus by this algorithm and at least 4 limit cycles by asymptotic expansions of the related Melnikov functions.