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Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system

Author

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  • Feng, Li
  • Yirong, Liu
  • Hongwei, Li

Abstract

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of septic polynomial differential systems are investigated. With the help of computer algebra system MATHEMATICA, the first 13 quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The result that there exist 13 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 septic Lyapunov systems.

Suggested Citation

  • Feng, Li & Yirong, Liu & Hongwei, Li, 2011. "Center conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(12), pages 2595-2607.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:12:p:2595-2607
    DOI: 10.1016/j.matcom.2011.05.001
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    Cited by:

    1. Giné, Jaume, 2016. "Center conditions for nilpotent cubic systems using the Cherkas method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 129(C), pages 1-9.

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