Chinese Quarterly Journal of Mathematics ›› 2011, Vol. 26 ›› Issue (1): 144-151.

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The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z2-symmetry Perturbation

  

  1. School of Mathematical Sciences, Xuchang University
  • Received:2007-04-16 Online:2011-03-30 Published:2023-05-15
  • About author:ZHOU Hong-xian(1978- ), male, native of Nanyang, Henan, a lecturer of Xuchang University, Ph.D., engages in differential equations and dynamical systems.
  • Supported by:
     Supported by the Natural Science Foundation of China(10802043,10826092);

Abstract: This paper is concerned with the number and distributions of limit cycles of a cubic Z2-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C19...C12)].

Key words: limit cycles, bifurcation, detection functions, Hamiltonian system

CLC Number: