Fourteen Limit Cycles in a Seven‐Degree Nilpotent System

Wentao Huang, Ting Chen and Tianlong Gu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/398609

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:398609

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