On the Number of Limit Cycles of a Class of Near-Hamiltonian Systems with a Nilpotent Center

被引:0
作者
Liu, Chenxi [1 ]
Liu, Huimei [1 ]
Li, Feng [1 ]
Cai, Meilan [1 ]
机构
[1] Linyi Univ, Sch Math & Stat, Linyi 276000, Shandong, Peoples R China
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2025年
基金
中国国家自然科学基金;
关键词
Bifurcation; Melnikov function; limit cycle; nilpotent center; BIFURCATION;
D O I
10.1142/S0218127425500683
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we consider a class of near-Hamiltonian systems with a nilpotent center, and study the number of limit cycles including algebraic limit cycles. We prove that there are at most n(m + 1) + 1 large amplitude limit cycles if the first-order Melnikov function is not zero identically, including an algebraic limit cycle. Moreover, it can have n(n+3)/2 when m >= n and m(2n-m+1)/2 + n when m < n small limit cycles. We also provide two examples as applications of our main results.
引用
收藏
页数:11
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