[1] |
Arnold L,Wihstutz V.Lyapunov Exponents[M].Lecture Notes in Mathematics,1186.Berlin:Springer-Verlag,1986.
|
[2] |
Arnold L,Crauel H,Eckmann J P.Lyapunov Exponents[M],Lecture Notesin Mathe matics,1486.Berlin:Springer-Verlag,1991.
|
[3] |
刘先斌.随机力学系统的分叉行为与变分方法研究[D].博士学位论文.成都:西南交通大学,1995.
|
[4] |
刘先斌,陈虬,陈大鹏.非线性随机动力学系统的稳定性和分岔研究[J].力学进展,1996,26(4):437~53.
|
[5] |
陈虬,刘先斌.随机稳定性和随机分岔研究进展[R].第七届现代数学和力学大会邀请报告.1997年11 月,上海.
|
[6] |
Khasminskii R Z.Stochastic Stability of Differential Equations[M].Alphenaan den Rijin,the Netherlands:Sijthoff and Noord hoff,1980.
|
[7] |
Arnold L,Papanicolaou G,Wihstutz V.Asymptotic analysis of the Lyapunov exponentsand rotation numbers of the random oscillator and applications[J].SIAM J Appl Math,1986,46(3):427~450.
|
[8] |
Arnold L.Lyapunov exponents of nonlinear stochastic systems[A].In:F Ziegler,GI Schuellereds.Nonlinear Stochastic Dynamic Engrg Systems,Berlin,New York:Springer-Verlag,1987,181~203.
|
[9] |
Arnold L,Boxler P.Eigenvalues,bifurcation and center manifolds in the presence of noise[A].In:CM Dafermos,G Ladas,G.Papannico laoueds.Differential Equations[M].New York:Marcel Dekker Inc,1990,33~50.
|
[10] |
Ariaratnam S T,Xie W C.Sensitivity of pitchfork bifurcation to stochastic perturbation[J].Dyna & Stab Sys,1992,7(3):139~150.
|
[11] |
Ariaratnam S T,Xie W C.Lyapunov exponents and stochastic stability ofcoupled linearsystems underrealnoise excitation[J].ASME J Appl Mech,1992,59(3):664~673.
|
[12] |
Ariaratnam S T,Xie W C.Lyapunov exponents and stochastic stability of two-dimensional parametrically excited random systems[J].ASME J Appl Mech,1993,60(5):677~682.
|
[13] |
Kozin F.Stability of the Linear Stochaxtic Systems[M].Lecture Notes in Math,294.New York:Springer-Verlag,1972,186~229.
|
[14] |
Namachchivaya Sri N,Ariaratnam S T.Stochastically perturbed Hoph bifurcation[J].Int J Nonlinear Mech,1987,22(5):363~373.
|
[15] |
Namachchivaya Sri N.Stochastic stability of a gyropendulum underrandom verticalsup portexcitation[J].J Sound & Vib,1987,119(2):363~373.
|
[16] |
Namachchivaya Sri N.Hopf bifurcation in the presence of both parametric and externalstochastic excitation[J].A S M E J Appl Mech,1998,55(4):923~930.
|
[17] |
Namachchivaya Sri N,Talwar S.Maximal Lyapunov exponent and rotation number forst ochastically peturbed codimension two bifurcation[J].J Sound & Vib,1993,169(3):349~372.
|
[18] |
刘先斌,陈虬,陈大鹏.白噪声参激 Hopf 分岔系统的两次分岔研究[J].应用数学和力学,1997,18(9):779~788.
|
[19] |
刘先斌,陈虬.实噪声参激Hopf分岔系统研究[J].力学学报,1997,29(2):158~166.
|
[20] |
刘先斌,陈虬,孙训方.白噪声参激一类余维2分岔系统研究[J].力学学报,1997,29(5):563~572.
|
[21] |
Pardoux E,Wihstutz V.Lyapunov exponentand rotation number of two imensionallinear stochastic systems with small diffusion[J].SIAM J Appl Math,1988,48(2):442~457.
|
[22] |
朱位秋.随机振动[M].北京:科学出版社,1992.
|
[23] |
Roy R V.Stochastic averaging of oscillators excited by coloured Gaussian processes[J].Int J Nonlinear Mech,1994,29(4):461~475.
|
[24] |
Dygas M M K,Matkowsky B J,Schuss Z.Stochastic stability of nonlinear oscillators[J].SIAM J Appl Math,1988,48(5):1115~1127.
|