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高阶非线性动力系统全局分析——胞胞映射法应用

徐皆苏 徐健学

徐皆苏, 徐健学. 高阶非线性动力系统全局分析——胞胞映射法应用[J]. 应用数学和力学, 1985, 6(11): 953-962.
引用本文: 徐皆苏, 徐健学. 高阶非线性动力系统全局分析——胞胞映射法应用[J]. 应用数学和力学, 1985, 6(11): 953-962.
C. S. Hsu, Xu Jian-xue. The Global Analysis of Higher Order Non-linear Dynamical Systems and the Application of Cell-to-Cell Mapping Method[J]. Applied Mathematics and Mechanics, 1985, 6(11): 953-962.
Citation: C. S. Hsu, Xu Jian-xue. The Global Analysis of Higher Order Non-linear Dynamical Systems and the Application of Cell-to-Cell Mapping Method[J]. Applied Mathematics and Mechanics, 1985, 6(11): 953-962.

高阶非线性动力系统全局分析——胞胞映射法应用

The Global Analysis of Higher Order Non-linear Dynamical Systems and the Application of Cell-to-Cell Mapping Method

  • 摘要: 本文阐述高阶非线性动力系统全局分析和应用胞胞映射进行分析的一般特点,以及胞胞映射方法对于高阶系统全局分析的有效性;并具体进行了一个弱耦合van der Pol振荡系统的全局分析,确定系统具有两个稳定的极限环,并确定了整个四维空间被分为两个部分,这两部分分别是沿两个极限环运动的渐近稳定域(吸引域).
  • [1] Hsu,C,S.,A theory of cell-to-cell mapping for dynamical systems,J.Appl.Mech.,47(1980),931-939.
    [2] Hsu,C.S.and R.S.Guttalu.An unravelling algorithm for global analysis of dynamical systems:An application of cell-to-cell mappings,J.Appl.Mech.,47(1980),940-948.
    [3] Hsu,C.S.,A generalized theory of cell-to-cell mapping for nonlinear dynamical systems,J.Appl.Mech.,48(1981),634-642.
    [4] Hsu,C.S.R.S.Guttalu and W.H.Zhu.A method of analyzing generalized cell mapping.,J.Appl.Mech..49(1982),885-895.
    [5] Hsu,C.S.,A probabilistic theory of nonlinear dynamical systems based on the cell state space concept,J.Appl.Mech..49(1982),895-902.
    [6] Kauderer,H.,Nichtlineare Mechanik,Springer(1958).
    [7] Yang,T.K.and R.M.Rosenberg,On forced vibrations of a particle in the plane,Int.J.Non-Linear Mech.,3(1968),47-63.
    [8] Pavlidis,T.,Biological Oscillators:Their Mathemetical Analysis,Academic Press(1973).
    [9] Rand,R.H.and P.J.Holmes,Bifurcation of periodic motions in two weakly coupled van der Pol oscillators,Int.J.Non-Linear Mech.,15(1980),387-399.
    [10] Hirsch,M.W.,C.C.Pugh and M.Shub,Invariant Manifolds,springer Lecture Notes in Math.No.583,Springer Verlag(1977).
    [11] Chillingworth,D.R.J.,Differential Topology with a View to Applications,Pitman,London (1976).
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出版历程
  • 收稿日期:  1985-01-05
  • 刊出日期:  1985-11-15

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