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Volumn 38, Issue 10, 2003, Pages 1495-1511

The Lyapunov exponent for a codimension two bifurcation system that is driven by a real noise

Author keywords

Asymptotic analysis; Detailed balance condition; Eigenfunction expansion; Linear filter system; Maximal Lyapunov exponent

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; LYAPUNOV METHODS; VECTORS;

EID: 0037413141     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00085-9     Document Type: Article
Times cited : (12)

References (21)
  • 1
    • 0002867279 scopus 로고
    • Lyapunov exponents of nonlinear stochastic systems
    • F. Ziegler, & G.I. Schueller. Berlin: Springer
    • Arnold L. Lyapunov exponents of nonlinear stochastic systems. Ziegler F., Schueller G.I. Nonlinear Stochastic Dynamic Engineering Systems. 1987;181-203 Springer, Berlin.
    • (1987) Nonlinear Stochastic Dynamic Engineering Systems , pp. 181-203
    • Arnold, L.1
  • 3
    • 0001549366 scopus 로고
    • Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems
    • Khasminskii R.Z. Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems. Theory Probab. Appl. 12(1):1967;144-147.
    • (1967) Theory Probab. Appl. , vol.12 , Issue.1 , pp. 144-147
    • Khasminskii, R.Z.1
  • 4
    • 0001479882 scopus 로고
    • Necessary and sufficient conditions for almost sure sample stability of linear Ito equations
    • Kozin F., Prodromou S. Necessary and sufficient conditions for almost sure sample stability of linear Ito equations. SIAM J. Appl. Math. 21:1971;413-424.
    • (1971) SIAM J. Appl. Math , vol.21 , pp. 413-424
    • Kozin, F.1    Prodromou, S.2
  • 5
    • 0016347319 scopus 로고
    • Sample stability of second order linear differential equations with wide band noise coefficients
    • Mitchell R.R., Kozin F. Sample stability of second order linear differential equations with wide band noise coefficients. SIAM J. Appl. Math. 27:1974;571-605.
    • (1974) SIAM J. Appl. Math. , vol.27 , pp. 571-605
    • Mitchell, R.R.1    Kozin, F.2
  • 6
    • 84972500225 scopus 로고
    • On the stability of two-dimensional linear stochastic systems
    • Nishoka K. On the stability of two-dimensional linear stochastic systems. Kodai Math. Sem. Rep. 27:1976;211-230.
    • (1976) Kodai Math. Sem. Rep. , vol.27 , pp. 211-230
    • Nishoka, K.1
  • 7
    • 0025056345 scopus 로고
    • Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system
    • Ariaratnam S.T., Xie W.C. Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system. Dyn. Stability Systems. 5(1):1990;1-9.
    • (1990) Dyn. Stability Systems , vol.5 , Issue.1 , pp. 1-9
    • Ariaratnam, S.T.1    Xie, W.C.2
  • 8
    • 0026917425 scopus 로고
    • Lyapunov exponents and stochastic stability of coupled linear systems under real noise excitation
    • Ariaratnam S.T., Xie W.C. Lyapunov exponents and stochastic stability of coupled linear systems under real noise excitation. ASME J. Appl. Mech. 59:1992;664-673.
    • (1992) ASME J. Appl. Mech. , vol.59 , pp. 664-673
    • Ariaratnam, S.T.1    Xie, W.C.2
  • 9
    • 0022737468 scopus 로고
    • Asymptotic analysis of the Lyapunov exponents and rotation numbers of the random oscillator and applications
    • Arnold L., Papanicolaou G., Wihstutz V. Asymptotic analysis of the Lyapunov exponents and rotation numbers of the random oscillator and applications. SIAM J. Appl. Math. 46(3):1986;427-450.
    • (1986) SIAM J. Appl. Math. , vol.46 , Issue.3 , pp. 427-450
    • Arnold, L.1    Papanicolaou, G.2    Wihstutz, V.3
  • 10
    • 0022734329 scopus 로고
    • Instability of the harmonic oscillator with small noise
    • Pinsky M.A. Instability of the harmonic oscillator with small noise. SIAM J. Appl. Math. 46(3):1986;451-463.
    • (1986) SIAM J. Appl. Math. , vol.46 , Issue.3 , pp. 451-463
    • Pinsky, M.A.1
  • 11
    • 0028259487 scopus 로고
    • Maximal Lyapunov exponent and rotation number for stochastically perturbed co-dimension two bifurcation
    • Sri. Namachchivaya N., Talwar S. Maximal Lyapunov exponent and rotation number for stochastically perturbed co-dimension two bifurcation. J. Sound Vibration. 169(3):1993;349-372.
    • (1993) J. Sound Vibration , vol.169 , Issue.3 , pp. 349-372
    • Namachchivaya, N.Sri.1    Talwar, S.2
  • 12
    • 21144461048 scopus 로고
    • Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise
    • Namachchivaya N.Sri., Van Roessel H.J. Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise. J. Stat. Phys. 71(3-4):1993;549-567.
    • (1993) J. Stat. Phys. , vol.71 , Issue.3-4 , pp. 549-567
    • Namachchivaya, N.Sri.1    Van Roessel, H.J.2
  • 13
    • 21344488886 scopus 로고
    • Almost-sure asymptotic stability of a general four dimensional dynamical system driven by real noise
    • Doyle M.M., Namachchivaya N.Sri. Almost-sure asymptotic stability of a general four dimensional dynamical system driven by real noise. J. Stat. Phys. 75:1994;525-552.
    • (1994) J. Stat. Phys. , vol.75 , pp. 525-552
    • Doyle, M.M.1    Namachchivaya, N.Sri.2
  • 15
    • 0018924713 scopus 로고
    • Extension of Eigenfunction-expansion solutions of a Fokker-Planck equation - II. Second order system
    • James P., Scott R.A. Extension of Eigenfunction-expansion solutions of a Fokker-Planck equation - II. Second order system. Int. J. Non-Linear Mech. 15:1980;41-56.
    • (1980) Int. J. Non-Linear Mech. , vol.15 , pp. 41-56
    • James, P.1    Scott, R.A.2
  • 16
    • 0028468266 scopus 로고
    • Stochastic averaging of oscillators excited by coloured Gaussian processes
    • Roy R.V. Stochastic averaging of oscillators excited by coloured Gaussian processes. Int. J. Non-Linear Mech. 29(4):1994;461-475.
    • (1994) Int. J. Non-Linear Mech. , vol.29 , Issue.4 , pp. 461-475
    • Roy, R.V.1
  • 18
    • 0028467015 scopus 로고
    • Stochastic stability of nonlinear systems
    • Lin Y.K., Cai G.Q. Stochastic stability of nonlinear systems. Int. J. Non-Linear Mech. 29(4):1994;539-553.
    • (1994) Int. J. Non-Linear Mech. , vol.29 , Issue.4 , pp. 539-553
    • Lin, Y.K.1    Cai, G.Q.2
  • 20
    • 0000438813 scopus 로고
    • Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion
    • Pardoux E., Wihstutz V. Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion. SIAM J. Appl. Math. 48(2):1988;442-457.
    • (1988) SIAM J. Appl. Math. , vol.48 , Issue.2 , pp. 442-457
    • Pardoux, E.1    Wihstutz, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.