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Limit Cycles and Integrability of a Class of Quintic System

Author

Listed:
  • Yanli Tang

    (Center for International Education, Philippine Christian University, Manila 1004, Philippines
    School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

  • Dongmei Zhang

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

  • Feng Li

    (School of Mathematics and Statistics, Linyi University, Linyi 276005, China)

Abstract

In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is proved. Meanwhile, bifurcation of limit cycles is discussed, 13 limit cycles can be bifurcated from the origin. As far as the number of limit cycles enclosing an isolated singular point is concerned, this is so far the best result for elementary singular points.

Suggested Citation

  • Yanli Tang & Dongmei Zhang & Feng Li, 2022. "Limit Cycles and Integrability of a Class of Quintic System," Mathematics, MDPI, vol. 10(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2993-:d:892364
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    References listed on IDEAS

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    1. Wu, Yuhai & Gao, Yongxi & Han, Maoan, 2008. "Bifurcations of the limit cycles in a z3-equivariant quartic planar vector field," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1177-1186.
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