一类单摆方程的Poincaré 分支

一类单摆方程的Poincaré 分支

The Poincaré Bifurcation of a Class of Pendulum Equations

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 843-849.

徐俊文,吴红星,孙杨剑^*()

上饶师范学院数学与计算机学院江西上饶 334001

收稿日期:2023-03-27 修回日期:2025-02-19 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *孙杨剑，Email: syj1508556017@163.com
基金资助:
江西省教育厅科技项目(GJJ211737);江西省教育厅科技项目(GJJ201714)

Xu Junwen,Wu Hongxing,Sun Yangjian^*()

School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi Shangrao 334001

Received:2023-03-27 Revised:2025-02-19 Online:2025-06-26 Published:2025-06-20
Supported by:
Foundation of Education Department of Jiangxi(GJJ211737);Foundation of Education Department of Jiangxi(GJJ201714)

摘要：

该文主要研究了一类单摆方程在二阶三角多项式扰动下产生的极限环个数. 通过改进相应的 Abelian 积分零点个数上界判别法, 可以得出其包含原点的周期环域至多分支出 2 个极限环 (计重数).

关键词: 单摆方程, Poincaré 分支, Abelian 积分, 极限环

Abstract:

In this paper, we mainly study the number of limit cycles bifurcate form the periodic orbits of pendulum equations under the perturbations for trigonometric polynomials of degree two. By improving the criterion function of determining the lowest upper bound of the number of zeros of Abelian Integrals, we show that the period annulus (around the origin) can be bifurcate at most two limit cycle (counting multiplicities).

Key words: pendulum equation, poincaré bifurcation, Abelian integral, limit cycle

中图分类号:

徐俊文, 吴红星, 孙杨剑. 一类单摆方程的Poincaré 分支[J]. 数学物理学报, 2025, 45(3): 843-849.

Xu Junwen, Wu Hongxing, Sun Yangjian. The Poincaré Bifurcation of a Class of Pendulum Equations[J]. Acta mathematica scientia,Series A, 2025, 45(3): 843-849.

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