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Fourteen Limit Cycles in a Seven-Degree Nilpotent System

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  • Wentao Huang
  • Ting Chen
  • Tianlong Gu

Abstract

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.

Suggested Citation

  • Wentao Huang & Ting Chen & Tianlong Gu, 2013. "Fourteen Limit Cycles in a Seven-Degree Nilpotent System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, November.
    • Handle: RePEc:hin:jnlaaa:398609
    DOI: 10.1155/2013/398609
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