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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

Software:

Mathematica
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Full Text: DOI

References:

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