**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31830

##### Ten Limit Cycles in a Quintic Lyapunov System

**Authors:**
Li Feng

**Abstract:**

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.

**Keywords:**
Three-order nilpotent critical point,
center-focus problem,
bifurcation of limit cycles,
Quasi-Lyapunov constant.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334726

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