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**A quintic polynomial differential system with eleven limit cycles at the infinity.**
*(English)*
Zbl 1152.34329

Summary: In this article, a recursion formula for computing the singular point quantities of the infinity in a class of quintic polynomial systems is given. The first eleven singular point quantities are computed with the computer algebra system Mathematica. The conditions for the infinity to be a center are derived as well. Finally, a system that allows the appearance of eleven limit cycles in a small enough neighborhood of the infinity is constructed.

### MSC:

34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |

34-04 | Software, source code, etc. for problems pertaining to ordinary differential equations |

### Keywords:

infinity; quintic system; singular point quantities; center conditions; bifurcation of limit cycles### Software:

Mathematica
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XMLCite

\textit{Q. Zhang} and \textit{Y. Liu}, Comput. Math. Appl. 53, No. 10, 1518--1526 (2007; Zbl 1152.34329)

Full Text:
DOI

### References:

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