双曲极限环在周期扰动下次调和解的分支

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Bifurcations of Subharmonic Solutions in Periodic Perturbation of a Hyperbolic Limit Cycle

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P.R.China

摘要: 研究了一给定平面自治系统的双曲极限环在周期扰动下m阶次调和解的分支问题,用Poincar啨映射,通过变尺度方法,获得了判别m阶次调和解的存在条件,最后给出了一个实例。
- 极限环 /
- 次调和解 /
- 分支
Abstract: Bifurcations of subharmonic solutions of order m of a planar periodic perturbed system near a hyperbolic limit cycle are discussed.By using a Poincar 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.
- bifurcation /
- subharmonic solution /
- limit cycle

[1]	HAN Mao-an. Periodic perturbations of planar systems with a semistable limit cycle[J]. Chin Sci Bull,1997,42(2):265-269.
[2]	韩茂安. 周期扰动系统不变环面和亚调和解的分支[J]. 中国科学(A辑),1994,37(11):1152-1160.
[3]	韩茂安,朱德明. 微分方程分支理论[M]. 第九章.北京:煤炭工业出版社,1994.