Algebraic Limit Cycle of Degree 2 for Linear Type Center Plus Cubic Homogeneous Polynomial Differential Systems

被引：0
|
作者：
Luping Wang [1 ]
Yuzhou Tian [2 ]
Yulin Zhao [1 ]
机构：
[1] Wang, Luping
[2] Tian, Yuzhou
[3] Zhao, Yulin
来源：
Zhao, Yulin (mcszyl@mail.sysu.edu.cn) | 2025年 / 31卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Invariant algebraic curve; Algebraic limit cycles; Rotated vector fields; Primary: 34C07; Secondary: 34C05;
D O I：
10.1007/s10883-024-09722-z
中图分类号：
学科分类号：
摘要：
In this paper, we study the algebraic limit cycle of degree 2 for the system x˙=-y+a30x3+a21x2y+a12xy2+a03y3, y˙=x+b30x3+b21x2y+b12xy2+b03y3, which is called a linear type center plus cubic homogeneous polynomial differential system. We derive the normal form of this system with an algebraic limit cycle of degree 2. It is shown that, if an invariant algebraic curve of degree 2 is a limit cycle of the above mentioned system, then it is a unique limit cycle in the phase plane. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
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