北京大学学报（自然科学版） ›› 2016, Vol. 52 ›› Issue (4): 653-657.DOI: 10.13209/j.0479-8023.2016.067

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一类非自治广义 Birkhoff 系统的稳定性和分岔

曹秋鹏1, 陈向炜2   

  1. 1. 苏州科技大学数理学院, 苏州 215009
    2. 商丘师范学院物理与电气信息学院, 商丘 476000
  • 收稿日期:2015-10-08 修回日期:2016-02-05 出版日期:2016-07-20 发布日期:2016-07-20
  • 通讯作者: 陈向炜, E-mail: hnchenxw(at)163.com
  • 基金资助:
    国家自然科学基金(11372169)和苏州科技大学研究生科研创新计划(SKCX14_056)资助

Stability and Bifurcation for a Type of Non-autonomous Generalized Birkhoffian Systems

CAO Qiupeng1, CHEN Xiangwei2   

  1. 1. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009
    2. Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000
  • Received:2015-10-08 Revised:2016-02-05 Online:2016-07-20 Published:2016-07-20
  • Contact: CHEN Xiangwei, E-mail: hnchenxw(at)163.com

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摘要：

研究一类非自治广义Birkhoff 系统的分岔。将该系统转化为梯度系统, 利用梯度系统的性质研究这一类系统平衡点的稳定性。研究表明, 当系统含有某个参数时, 系统平衡点的数目和稳定性将会随参数的变化而发生改变, 从而产生分岔现象。

关键词: 广义 Birkhoff 系统, 梯度系统, 分岔

Abstract:

Bifurcation for a type of non-autonomous generalized Birkhoffian systems is studied. Gradient representations for this type of non-autonomous generalized Birkhoffian systems are given. The stability of equilibrium point of these systems is discussed by the characteristic of the gradient system. Further the systems which contain some parameter are studied. The stability and the number of equilibrium point will change along with the change of the parameter to produce the bifurcation phenomenon.

Key words: generalized Birkhoffian system, gradient system, bifurcation

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