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Volumn 30, Issue 4, 2002, Pages 313-321

Invariant measures and Lyapunov exponents for stochastic Mathieu system

Author keywords

Almost sure sample stability; Maximum Lyapunov exponent; Multiple scale method; Principal resonance; Stochastic Mathieu system

Indexed keywords

ASYMPTOTIC STABILITY; BESSEL FUNCTIONS; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; DAMPING; INTEGRATION; LYAPUNOV METHODS; MONTE CARLO METHODS; OSCILLATORS (ELECTRONIC); PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

EID: 0036926475     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021208631414     Document Type: Article
Times cited : (19)

References (18)
  • 1
    • 0001549366 scopus 로고
    • Necessary and sufficient conditions for asymptotic stability of linear stochastic system
    • Khasminskii, R. Z., 'Necessary and sufficient conditions for asymptotic stability of linear stochastic system'. Theory of Probability and Its Applications 12, 1967. 144-147.
    • (1967) Theory of Probability and Its Applications , vol.12 , pp. 144-147
    • Khasminskii, R.Z.1
  • 2
    • 0001178181 scopus 로고
    • Stability of linear stochastic systems
    • in Stability of Stochastic Dynamical Systems, R. Curtain (ed.); Springer-Verlag, New York
    • Kozin, F., 'Stability of linear stochastic systems', in Stability of Stochastic Dynamical Systems, R. Curtain (ed.), Lecture Notes in Mathematics, Vol. 294, Springer-Verlag, New York, 1972, pp. 186-229.
    • (1972) Lecture Notes in Mathematics , vol.294 , pp. 186-229
    • Kozin, F.1
  • 3
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems
    • Oseledec, V. I., 'A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems', Transaction of the Moscow Mathematical Society 19, 1968, 197-231.
    • (1968) Transaction of the Moscow Mathematical Society , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 4
    • 0002716381 scopus 로고
    • Qualitative theory of stochastic systems
    • A. T. Bharucha-Reid (ed.), Academic Press, New York
    • Arnold, L. and Kliemann, W., 'Qualitative theory of stochastic systems', in Probabilistic Analysis and Related Topics, Vol. 3, A. T. Bharucha-Reid (ed.), Academic Press, New York, 1981, pp. 281-287.
    • (1981) Probabilistic Analysis and Related Topics , vol.3 , pp. 281-287
    • Arnold, L.1    Kliemann, W.2
  • 5
    • 0001980139 scopus 로고
    • Stability of linear differential systems with parametric excitation
    • F. Ziegler and G. I. Schueller (eds.), Springer-Verlag, Berlin
    • Pardoux, E. and Talay, D., 'Stability of linear differential systems with parametric excitation', in Nonlinear Stochastic Dynamic Engineering Systems, F. Ziegler and G. I. Schueller (eds.), Springer-Verlag, Berlin, 1988, pp. 153-168.
    • (1988) Nonlinear Stochastic Dynamic Engineering Systems , pp. 153-168
    • Pardoux, E.1    Talay, D.2
  • 6
    • 0025452258 scopus 로고
    • Invariant measures and lyapunov exponents for generalized parameter fluctuations
    • Wedig, W. V., 'Invariant measures and Lyapunov exponents for generalized parameter fluctuations'. Structural Safety 8, 1990, 13-25.
    • (1990) Structural Safety , vol.8 , pp. 13-25
    • Wedig, W.V.1
  • 8
    • 0024034644 scopus 로고
    • Multiple time scaling of the response of a duffing oscillator to narrow-band excitations
    • Rajan, S. and Davies, H. G., 'Multiple time scaling of the response of a Duffing oscillator to narrow-band excitations', Journal of Sound and Vibration 123, 1988, 497-506.
    • (1988) Journal of Sound and Vibration , vol.123 , pp. 497-506
    • Rajan, S.1    Davies, H.G.2
  • 9
    • 0025673024 scopus 로고
    • Response statistics of nonlinear systems to combined deterministic and random excitations
    • Nayfeh, A. H. and Serhan, S. J., 'Response statistics of nonlinear systems to combined deterministic and random excitations'. International Journal of Non-Linear Mechanics 25(5), 1990, 493-509.
    • (1990) International Journal of Non-Linear Mechanics , vol.25 , Issue.5 , pp. 493-509
    • Nayfeh, A.H.1    Serhan, S.J.2
  • 10
    • 0001201564 scopus 로고    scopus 로고
    • Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation
    • Rong, H. W., Xu, W., and Fang T., 'Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation', Journal of Sound and Vibration 210(4), 1998, 483-515.
    • (1998) Journal of Sound and Vibration , vol.210 , Issue.4 , pp. 483-515
    • Rong, H.W.1    Xu, W.2    Fang, T.3
  • 13
    • 0000753370 scopus 로고
    • Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation
    • Dimentberg, M., 'Stability and subcritical dynamics of structures with spatially disordered travelling parametric excitation', Probabilistic Engineering Mechanics 7, 1992, 131-134.
    • (1992) Probabilistic Engineering Mechanics , vol.7 , pp. 131-134
    • Dimentberg, M.1
  • 14
    • 0012345873 scopus 로고
    • Stability of a SDOF system under periodic parametric excitation with a white-noise phase modulation
    • W. Kliemann and N. Sri Namachivaya (eds.), CRC Press Mathematical Modelling Series, CRC Press, New York
    • Dimentberg, M., Hou, Z., and Noori, M., 'Stability of a SDOF system under periodic parametric excitation with a white-noise phase modulation', in Stochastic and Nonlinear Dynamics: Application to Mechanical Systems, W. Kliemann and N. Sri Namachivaya (eds.), CRC Press Mathematical Modelling Series, CRC Press, New York, 1995, pp. 341-359.
    • (1995) Stochastic and Nonlinear Dynamics: Application to Mechanical Systems , pp. 341-359
    • Dimentberg, M.1    Hou, Z.2    Noori, M.3
  • 15
    • 0022737468 scopus 로고
    • Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and application
    • Arnold, L., Papanicolaou, G., and Wihstutz, V., 'Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and application', SIAM Journal of Applied Mathematics 46, 1986, 427-450.
    • (1986) SIAM Journal of Applied Mathematics , vol.46 , pp. 427-450
    • Arnold, L.1    Papanicolaou, G.2    Wihstutz, V.3
  • 16
    • 0000438813 scopus 로고
    • Lyapunov exponent and rotation number of the two dimensional linear stochastic systems with small diffusion
    • Pardoux, E. and Wihstutz, V., 'Lyapunov exponent and rotation number of the two dimensional linear stochastic systems with small diffusion', SIAM Journal of Applied Mathematics 48, 1988, 442-457.
    • (1988) SIAM Journal of Applied Mathematics , vol.48 , pp. 442-457
    • Pardoux, E.1    Wihstutz, V.2
  • 18
    • 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 of Probability and Its Applications 12, 1967, 144-147.
    • (1967) Theory of Probability and Its Applications , vol.12 , pp. 144-147
    • Khasminskii, R.Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.