Open Access
2013 Fourteen Limit Cycles in a Seven-Degree Nilpotent System
Wentao Huang, Ting Chen, Tianlong Gu
Abstr. Appl. Anal. 2013: 1-5 (2013). DOI: 10.1155/2013/398609


Center conditions and the bifurcation of limit cycles for a seven-degree polynomial differential system in which the origin is a nilpotent critical point are studied. Using the computer algebra system Mathematica, the first 14 quasi-Lyapunov constants of the origin are obtained, and then the conditions for the origin to be a center and the 14th-order fine focus are derived, respectively. Finally, we prove that the system has 14 limit cycles bifurcated from the origin under a small perturbation. As far as we know, this is the first example of a seven-degree system with 14 limit cycles bifurcated from a nilpotent critical point.


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Wentao Huang. Ting Chen. Tianlong Gu. "Fourteen Limit Cycles in a Seven-Degree Nilpotent System." Abstr. Appl. Anal. 2013 1 - 5, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1298.34062
MathSciNet: MR3129329
Digital Object Identifier: 10.1155/2013/398609

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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