Liu Xianbin, Chen Qiu, Chen Dapeng. On the Two Bifurcatinos of a White-Noise Excited Hopf Bifurcation System[J]. Applied Mathematics and Mechanics, 1997, 18(9): 779-788.
Citation: Liu Xianbin, Chen Qiu, Chen Dapeng. On the Two Bifurcatinos of a White-Noise Excited Hopf Bifurcation System[J]. Applied Mathematics and Mechanics, 1997, 18(9): 779-788.

On the Two Bifurcatinos of a White-Noise Excited Hopf Bifurcation System

  • Received Date: 1996-03-06
  • Rev Recd Date: 1997-05-03
  • Publish Date: 1997-09-15
  • The present work is concerned with the behavior of the second bifurcation of aHopf bifurcation system excited by white-noise. It is found that the intervention ofnoises induces a drift of the bifurcation point along with the subtantial change inbifurcation type.
  • loading
  • [1]
    G.Nicolis and I.Prigogine,Self-Orgamzation in Nonequilibrium Systems.Wiley,NewYork(1977).
    [2]
    H.Haken,Synergetics,Springer-Verlag,Berlin(1977).
    [3]
    R.Graham,Stochastic methods in nonequilibrium thermodynamics,in L.Arnold et al.eds.,Stochastic Nonlinear Systems in Physics,Chemiatry and Biotogy,Berlin,3pringer-Verlag(1981),202~212.
    [4]
    C.Meunier and A.D.Verga.Noise and bifurcation,J.Stat.Phys.,50,1~(1988),345~375.
    [5]
    N.Sri Namachchivaya,Stochastic bifurcation,APPl.Math.& Compt.,38(1990),101~159.
    [6]
    L.Arnold,Lyapunov exponents of nonlinear stochastic systems,Nonlinear StochasticDynamic Engrg.Systeins,F.Ziegler and G.I.Schueller eds.,Springer-Verlag,Berlin,New York(1987),181~203.
    [7]
    R.Z.Khasminskii,Necessary and sufficient conditions for the asymptotic stabilitv oflinear stochastic systems,Theory Prob.& APPl.,12,1(1967),144~147.
    [8]
    R.Z.Khasminskii,Stochastic Stability of Differential Equations,Sijthoff and Noordloff.Alphen aan den Rijn,the Netherlands,Rockville,Maryland.USA(1980).
    [9]
    L.Arnold and V.Wihstutz,eds.,Lyapunov exponents,Proc.of a Workshop,held inBremen,November 12~15,1984,Springer-Verlag,Berlin,Heidelberg(1986).
    [10]
    S.T.Ariaratnam and W.C.Xie,Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system,Dyna.& Stab.Sys.,5,1(1990),1~9.
    [11]
    S.T.Ariaratnam,D.S.F.Tam and W.C.Xie,Lyapunov exponents of two-degree-of-freedom linear stochastic systems,Stochastic Structural Dynamics l,Y.K.Lin and I.Elishakoff eds.,Springer-Verlag,Berlin(1991),1~9.
    [12]
    N.Sri Namachchivaya and S.Talwar,Maximal Lyapunov exponent and rotationnumber for stochastically perturbed co-dimension two bifurcation,J.Sound & Vib,.169.3(1993),349~372.
    [13]
    L.Arnold and W.Kliemann,Qualitative theory of stochastic systems,Prob.Anal.andRelaled Topics.A.T.Bharucha-Reid eds.Academic Press,New York,Lindon.3(1983).1~79.
    [14]
    Z.Schuss,Theory and APPlications of Stochaslic Differential Equations,John Wiley &Sons,New York(1980).
    [15]
    K.Ito and H.P.McKean,Jr.,Diffusion Processes and Tleir Sample Paths.Springer-Verlag,New York(1965).
    [16]
    S.Karlin and H.M.Taylor,A Second Course in Stochastic Processes,Academic Press.New York(1981).
    [17]
    F.Kozin and S.Prodromou,Necessary and sufficient conditions for almost sure samplestability of linear Ito equations,SIAM J.APPl.Math.,21(1971),413~424.
    [18]
    R.R.Mitchell and F.Kozin,Sample stability of second order linear differentialequations with wide band noise coefficients,SIAM.J.APPl.Math.,27(1974),571~605.
    [19]
    K.Nishoka,On the stability of two-dimensional linear stochastic systems-Kotlai Math.Sem.Rep.,27(1976),221~230.
    [20]
    徐利治、陈文忠,《渐近分析方法及应用》,国防工业出版社(1991).
    [21]
    尼科里斯、普利高津,《探索复杂性》(罗久里,陈奎宁泽),四川教育出版社,成都(1986).
    [22]
    刘先斌,《随机力学系统的分叉行为与变分方法研究》,西南交通大学博士学位论文,成都(1995).
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1957) PDF downloads(561) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return