期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类余维二向量场3-D解的存在性分析

Existence Analysis of 3-D Torus of Vector Fields Associated with Co-dimension Two
在线阅读 下载PDF
导出
摘要 分析了一类余维二向量场的分岔过程 首先基于系统的规范型,得到了不同的定常解,然后针对不同的分岔解运用稳定性判据,分别确定其稳定性条件,在参数平面上定义了临界曲线 于是就将参数空间划分为不同的区域,不同的区域和不同的分岔解相对应,由此给出了该系统3 D解存在的必要条件及证明 继而根据不同的情形。 The bifurcation behavior of vector field associated with codimension 2 is discussed. At first, based on the normal forms of the system, different steady state solutions are obtained. By applying the stability criteria to determine the stable conditions of respective bifurcation solutions, we define the critical curves on the parameter plane. The parameter subspace is divided into different regions according to different solutions. Then we verify the existing necessary conditions of 3D solutions. In the end the transition boundaries corresponding to different cases are sought.
作者 邹勇 路淼 毕勤胜
机构地区 江苏大学理学院
出处 《江苏大学学报（自然科学版）》 EI CAS 2003年第5期88-90,共3页 Journal of Jiangsu University：Natural Science Edition
基金 江苏省教育厅自然科学基金资助项目(01KJB110003)
关键词 3-D环面解 余维二 分岔 转迁集 3-D torus co-dimension two bifurcation transition boundary
分类号 O323 [理学—一般力学与力学基础]
  • 相关文献

参考文献6

  • 1毕勤胜,陈章耀,朱玉萍,邹勇.参数激励耦合系统的复杂动力学行为分析[J].力学学报,2003,35(3):367-372. 被引量：7
  • 2Dieci L, Lorenz J, Russell R D. Numerical Calculations of Invariant Tori for Two Weakly Coupled Van Der Pol Oscillators[ J ]. SIAM, J Sci Star Comput, 1990,12 : 607- 647.
  • 3Giisinn D E. Constructing Invariant Toil for Two Weakly Coupled Van Der Pol Oscillators [ J ]. Nonlinear Dynamics, 1995,8:269 - 305.
  • 4Qinsheng Bi, Yu P. Double Hopf Bifurcations and Chaos of a Nonlinear Vibration System[J ]. Nonlinear Dynamics, 1999, 19(4):294- 317.
  • 5Oinsheng Bi, Huihui Dai. Analysis of Nonlinear Dynamics and Bifurcations of a Shallow Arch Subjected to Periodic Excitation with Internal Resonance[J ]. Journal of Sound and Vibration, 2000, 233(4) :557 - 571.
  • 6Guckenheimer J, Holmes P J. Nonlinear Oscillations,Dynamical System and Bifurcations of Vector Fields[M]. New York: Springer-Verlag, 1983.

二级参考文献12

  • 1Maccari A. Approximation solution of a class of nonlinear oscillators in resonance with periodic excitation. Nonlinear Dynamics, 1998, 15:329-343.
  • 2Maccari A. Nonlinear oscillations with multiple resonant or non-resonant forcing terms, Int J Non-linear Mechanics,1999, 34:27-34.
  • 3Maccari A. Modulated motion and infinite-period bifurcation for two non-linearly coupled and parametrically excited van der Pol oscillators, Int J Non-linear Mechanics,2001, 36:335-347.
  • 4Wiggins S. Global Bifurcation and Chaos. New York:Springer, 1988.
  • 5Tien W, Namachchivaya NS, Medhotra N. Nonlinear dynamics of a shallow arch under periodic excitation-Ⅱ.l:linternal resonance, Int J Nonlinear Mechanics, 1994,29, 367-386.
  • 6Malhotra N, Namachchivaya NS. Global bifurcations in externally excited two-degree-of-freedom nonlinear systems.Nonlinear Dynamics, 1995, 8:85-109.
  • 7Bolotin W, Grishko AA, Kounadis AN, et al. Nonlinear panel flutter in remote post-critical domains,Int J Nonlinear Mechanics, 1998, 33:753-764.
  • 8Wolf A, Swift JB, Swinney HL, et al. Determining Lyapunov exponent from a time series. Physica D, 1985, 16:285-317.
  • 9Rand RH, Holmes PJ. Bifurcation of periodic motions into weakly coupled van der Pol oscillators. Int J Nonlinear Mechanics, 1980, 15:387-399.
  • 10Dieci L, Lorenz R, Russell RD. Numerical calculations of invariant tori for two weakly coupled van der Pol oscillators. SIAM J Sci Stat Comput, 1990, 12:607-647.

共引文献6

江苏大学学报（自然科学版）
2003年 第5期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部