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

doi:10.13209/j.0479-8023.2016.067

Acta Scientiarum Naturalium Universitatis Pekinensis ›› 2016, Vol. 52 ›› Issue (4): 653-657.DOI: 10.13209/j.0479-8023.2016.067

Previous Articles Next Articles

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

CAO Qiupeng¹, CHEN Xiangwei²

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

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. 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

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

Abstract

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

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

CLC Number:

O316

CAO Qiupeng, CHEN Xiangwei. Stability and Bifurcation for a Type of Non-autonomous Generalized Birkhoffian Systems[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 653-657.

曹秋鹏, 陈向炜. 一类非自治广义 Birkhoff 系统的稳定性和分岔[J]. 北京大学学报（自然科学版）, 2016, 52(4): 653-657.

Add to citation manager EndNote|Ris|BibTeX

URL: https://xbna.pku.edu.cn/EN/10.13209/j.0479-8023.2016.067

https://xbna.pku.edu.cn/EN/Y2016/V52/I4/653

[1]	MEI Fengxiang,WU Huibin,LI Yanmin. Two Kinds of Gradient Representations for Nielsen Equations [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2016, 52(4): 588-591.
[2]	XIAO Shifu,CHEN Bin,LIU Caishan. Dynamic Behavior and Buckling Analysis of Thin Rectangular Plate Rotating around Its Symmetrical Axis [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2005, 41(3): 373-380.
[3]	BAO Yangang,WU Jike. Continuation Method for Periodic Solution after Hopf Bifurcation [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1995, 31(5): 538-541.

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

一类非自治广义 Birkhoff 系统的稳定性和分岔

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 3

Recommended Articles

Metrics