当前位置：
X-MOL 学术
›
Proc. Am. Math. Soc.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
Global dynamics of a Wilson polynomial Liénard equation
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-30 , DOI: 10.1090/proc/15074 Haibo Chen , Hebai Chen
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-30 , DOI: 10.1090/proc/15074 Haibo Chen , Hebai Chen
Abstract:Gasull and Sabatini in [Ann. Mat. Pura Appl. 198 (2019), pp. 1985-2006] studied limit cycles of a Liénard system which has a fixed invariant curve, i.e., a Wilson polynomial Liénard system. The Liénard system can be changed into 
. For 
and 
, limit cycles of the system are studied completely. But for 
, the exact number of limit cycles is still unknown, and Gasull and Sabatini conjectured that the exact number of limit cycles is two (including multiplicities). In this paper, we give a positive answer to this conjecture and study all bifurcations of the system. Finally, we show the expanding of the moving limit cycle as 
increases and give all global phase portraits on the Poincaré disk of the system completely.
中文翻译：
Wilson多项式Liénard方程的整体动力学
摘要：[Ann.Gasull和Sabatini 垫。普拉应用 198（2019），第1985-2006页]研究了具有固定不变曲线的Liénard系统的极限环，即Wilson多项式Liénard系统。Liénard系统可以更改为。对和，系统的极限环进行了全面研究。但是对于，极限环的确切数目仍然未知，Gasull和Sabatini推测极限环的精确数目为2（包括多重性）。在本文中，我们对此猜想给出了肯定的答案，并研究了系统的所有分叉。最后，我们显示了移动极限周期随增加而扩展，并在系统的庞加莱磁盘上完全给出了所有全局相位肖像。
更新日期：2020-09-02
. For and , limit cycles of the system are studied completely. But for , the exact number of limit cycles is still unknown, and Gasull and Sabatini conjectured that the exact number of limit cycles is two (including multiplicities). In this paper, we give a positive answer to this conjecture and study all bifurcations of the system. Finally, we show the expanding of the moving limit cycle as increases and give all global phase portraits on the Poincaré disk of the system completely. 中文翻译：
Wilson多项式Liénard方程的整体动力学
摘要：[Ann.Gasull和Sabatini 垫。普拉应用 198（2019），第1985-2006页]研究了具有固定不变曲线的Liénard系统的极限环，即Wilson多项式Liénard系统。Liénard系统可以更改为。对和，系统的极限环进行了全面研究。但是对于，极限环的确切数目仍然未知，Gasull和Sabatini推测极限环的精确数目为2（包括多重性）。在本文中，我们对此猜想给出了肯定的答案，并研究了系统的所有分叉。最后，我们显示了移动极限周期随增加而扩展，并在系统的庞加莱磁盘上完全给出了所有全局相位肖像。
京公网安备 11010802027423号