Applied Mathematics and Mechanics

, Volume 23, Issue 8, pp 981–986 | Cite as

Bifurcations of subharmonic solutions in periodic perturbation of a hyperbolic limit cycle

  • HAN Mao-an
  • GU Sheng-shi


Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed. By using a Poincaré map and the method of rescaling a discriminating condition for the existence of subharmonic solutions of order m is obtained. An example is given in the end of the paper.

Key words

bifurcation subharmonic solution limit cycle 

CLC number



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  1. [1]
    HAN Mao-an. Periodic perturbations of planar systems with a semistable limit cycle[J].Chinese Sci Bull, 1997,42(2):265–269.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    HAN Mao-an. Bifurcations of invariant tori and subharmonic solutions for periodic perturbed systems[J].Science in China Ser A, 1994,37(11):1152–1160. (in Chinese)Google Scholar
  3. [3]
    HAN Mao-an, ZHU De-ming.Bifurcation Theory of Differential Equations[M]. Chapter 9. Beijing: Coal Industry Press, 1994. (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • HAN Mao-an
    • 1
  • GU Sheng-shi
    • 1
  1. 1.Department of MathematicsShanghai Jiaotong UniversityShanghaiP R China

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