数学物理学报(英文版)

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LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE

刘振海; E. Sáez; I. Szántó   

  1. 长沙理工大学数学系, 长沙 410076
  • 收稿日期:2006-03-22 修回日期:1900-01-01 出版日期:2008-10-20 发布日期:2008-10-20
  • 通讯作者: 刘振海
  • 基金资助:

    Financed partially by NNSF of China (10671211),NSF of Hunan Province (07JJ3005), and USM (120628 and 120627)

LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE

Liu Zhenhai; E. Sáez; I. Szántó   

  1. Department of Mathematics, Changsha University of Sciences and Technology, Changsha 410076, China
  • Received:2006-03-22 Revised:1900-01-01 Online:2008-10-20 Published:2008-10-20
  • Contact: Liu Zhenhai

摘要:

In this article, the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola. For this class of second-order differential systems, it is shown that for certain values of the
parameters the invariant parabola coexists with a center. For other values it can coexist with one, two or three small amplitude limit cycles which are constructed by Hopf bifurcation. This result gives an answer for the question given in [4], about the existence of limit cycles for such class of system.

关键词: Kukles system, limit cycles, invariant algebraic curves

Abstract:

In this article, the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola. For this class of second-order differential systems, it is shown that for certain values of the
parameters the invariant parabola coexists with a center. For other values it can coexist with one, two or three small amplitude limit cycles which are constructed by Hopf bifurcation. This result gives an answer for the question given in [4], about the existence of limit cycles for such class of system.

Key words: Kukles system, limit cycles, invariant algebraic curves

中图分类号: 

  • 92D25