Fourteen Limit Cycles in a Seven-Degree Nilpotent System | Zendy

Wentao Huang | Zendy; Ting Chen | Zendy; Tianlong Gu | Zendy

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Fourteen Limit Cycles in a Seven-Degree Nilpotent System

Author(s) -

Wentao Huang,

Ting Chen,

Tianlong Gu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/398609

Subject(s) - mathematics , nilpotent , bifurcation , perturbation (astronomy) , limit (mathematics) , degree (music) , limit cycle , ordinary differential equation , polynomial , pure mathematics , center (category theory) , critical point (mathematics) , mathematical analysis , differential equation , nonlinear system , chemistry , physics , quantum mechanics , acoustics , crystallography

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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