Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center

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• 作者：Junmin Yang^a ; Pei Yu ; ^b ; ^pyu@uwo.ca
• 关键词：Near-Hamiltonian system ; Nilpotent center ; Hopf bifurcation ; Limit cycle ; Normal form ; Generalized Lyapunov constant
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：298
• 期：Complete
• 页码：141-152
• 全文大小：496 K
• 卷排序：298

文摘

In this paper, we study bifurcation of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center. We use normal form theory to compute the generalized Lyapunov constants and show that there exist at least 9 limit cycles around the nilpotent center. This is a new lower bound on the number of limit cycles in planar cubic near-Hamiltonian systems with a nilpotent center.