메뉴 건너뛰기




Volumn 12, Issue 3, 1997, Pages 187-211

Small noise expansion of moment Lyapunov exponents for two-dimensional systems

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); DYNAMIC RESPONSE; ELECTRIC EXCITATION; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES;

EID: 0031223415     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119708806244     Document Type: Article
Times cited : (77)

References (25)
  • 2
    • 0021477394 scopus 로고
    • A formula connecting sample and moment stability of linear stochastic systems
    • Arnold, L. (1984) A formula connecting sample and moment stability of linear stochastic systems. SIAM Journal of Applied Mathematics 44, 793-802.
    • (1984) SIAM Journal of Applied Mathematics , vol.44 , pp. 793-802
    • Arnold, L.1
  • 4
    • 0001287714 scopus 로고
    • Large Deviations of Linear Stochastic Differential Equations
    • Springer, New York
    • Arnold, L. and Kliemann, W. (1987) Large Deviations of Linear Stochastic Differential Equations (Lecture Notes in Control and Information Sciences, 96; Springer, New York), pp. 117-151.
    • (1987) Lecture Notes in Control and Information Sciences , vol.96 , pp. 117-151
    • Arnold, L.1    Kliemann, W.2
  • 5
    • 0001881377 scopus 로고
    • Lyapunov Exponents of Linear Stochastic Systems
    • Springer, New York
    • Arnold, L., Kliemann, W. and Oeljeklaus, E. (1986) Lyapunov Exponents of Linear Stochastic Systems (Lecture Notes in Mathematics, 1186; Springer, New York), pp. 85-125.
    • (1986) Lecture Notes in Mathematics , vol.1186 , pp. 85-125
    • Arnold, L.1    Kliemann, W.2    Oeljeklaus, E.3
  • 6
    • 0001881373 scopus 로고
    • Almost Sure and Moment Stability for Linear Itô Equations
    • Springer, New York
    • Arnold, L., Oeljeklaus, E. and Pardoux, E. (1986) Almost Sure and Moment Stability for Linear Itô Equations (Lecture Notes in Mathematics, 1186; Springer, New York), pp. 129-159.
    • (1986) Lecture Notes in Mathematics , vol.1186 , pp. 129-159
    • Arnold, L.1    Oeljeklaus, E.2    Pardoux, E.3
  • 7
    • 0022737468 scopus 로고
    • Asymptotic analysis of Lyapunov exponent and rotation number of the random oscillator and applications
    • Arnold, L., Papanicolaou, G. and Wihstutz, V. (1986) Asymptotic analysis of Lyapunov exponent and rotation number of the random oscillator and applications. SIAM Journal of Applied Mathematics 46, 427-450.
    • (1986) SIAM Journal of Applied Mathematics , vol.46 , pp. 427-450
    • Arnold, L.1    Papanicolaou, G.2    Wihstutz, V.3
  • 9
    • 0002247469 scopus 로고
    • Moment stability and large deviations for linear stochastic differential equations
    • Kinokuniya, Tokyo
    • Baxendale, P. H. (1987) Moment stability and large deviations for linear stochastic differential equations. Taniguchi Symposium, Kinokuniya, Tokyo, pp. 31-54.
    • (1987) Taniguchi Symposium , pp. 31-54
    • Baxendale, P.H.1
  • 11
    • 0001053198 scopus 로고
    • Invariant Measures for Nonlinear Stochastic Differential Equations
    • Springer, New York
    • Baxendale, P. H. (1990) Invariant Measures for Nonlinear Stochastic Differential Equations (Lecture Notes in Mathematics, 1486; Springer, New York), pp. 123-140.
    • (1990) Lecture Notes in Mathematics , vol.1486 , pp. 123-140
    • Baxendale, P.H.1
  • 12
    • 21344488886 scopus 로고
    • Almost-sure asymptotic stability of a general four dimensional dynamical system driven by real noise
    • Doyle, M. M. and Sri Namachchivaya, N. (1994) Almost-sure asymptotic stability of a general four dimensional dynamical system driven by real noise. Journal of Statistical Physics 75, 525-552.
    • (1994) Journal of Statistical Physics , vol.75 , pp. 525-552
    • Doyle, M.M.1    Sri Namachchivaya, N.2
  • 13
    • 85024557581 scopus 로고
    • Stability of shallow arches against snap-through under time-wise step loads
    • Hsu, C. S. (1969) Stability of shallow arches against snap-through under time-wise step loads. AIAA Journal 35, 31-39.
    • (1969) AIAA Journal , vol.35 , pp. 31-39
    • Hsu, C.S.1
  • 14
    • 0042782938 scopus 로고
    • Relations between sample and moment stability for linear stochastic differential
    • ed. J. D. Mason; Academic Press, New York
    • Kozin, F. and Sugimoto, S. (1977) Relations between sample and moment stability for linear stochastic differential. Proceedings of Conference on Stochastic Differential Equations and Applications (ed. J. D. Mason; Academic Press, New York), pp. 145-162.
    • (1977) Proceedings of Conference on Stochastic Differential Equations and Applications , pp. 145-162
    • Kozin, F.1    Sugimoto, S.2
  • 16
    • 3042869202 scopus 로고
    • Coupled vibrations of mechanical systems under random actions
    • English translation from the Russian
    • Mirkina, A. S. (1974) Coupled vibrations of mechanical systems under random actions. Mathematics of Solids 9, 56-61 (English translation from the Russian).
    • (1974) Mathematics of Solids , vol.9 , pp. 56-61
    • Mirkina, A.S.1
  • 17
    • 0002297290 scopus 로고
    • The structure of eigenfunctions of one-dimensional unordered structures
    • Molcanov, S. A. (1978) The structure of eigenfunctions of one-dimensional unordered structures. Mathematics USSR Izvestija 12, 69-101.
    • (1978) Mathematics USSR Izvestija , vol.12 , pp. 69-101
    • Molcanov, S.A.1
  • 18
    • 0000438813 scopus 로고
    • Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion
    • Pardoux, E. and Wihstutz, V. (1988) Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion. SIAM Journal of Applied Mathematics 48, 442-457.
    • (1988) SIAM Journal of Applied Mathematics , vol.48 , pp. 442-457
    • Pardoux, E.1    Wihstutz, V.2
  • 19
    • 3042869201 scopus 로고
    • Lyapunov exponent and rotation number of the linear harmonic oscillator
    • (Stochastic Flows) (eds M. A. Pinsky and V. Wihstutz; Birkhäuser, Boston, MA)
    • Pinsky, M. A. (1992) Lyapunov exponent and rotation number of the linear harmonic oscillator. Diffusion Processes and Related Problems in Analysis, Volume II (Stochastic Flows) (eds M. A. Pinsky and V. Wihstutz; Birkhäuser, Boston, MA), pp. 257-267.
    • (1992) Diffusion Processes and Related Problems in Analysis , vol.2 , pp. 257-267
    • Pinsky, M.A.1
  • 21
    • 21144461048 scopus 로고
    • Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise
    • Sri Namachchivaya, N. and Van Roessel, H. J. (1993) Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise. Journal of Statistical Physics 71, 549-567.
    • (1993) Journal of Statistical Physics , vol.71 , pp. 549-567
    • Sri Namachchivaya, N.1    Van Roessel, H.J.2
  • 23
    • 0013298548 scopus 로고
    • On the rate at which a homogeneous diffusion approaches a limit, an application of the large deviation theory of certain stochastic integrals
    • Stroock, D. W. (1986) On the rate at which a homogeneous diffusion approaches a limit, an application of the large deviation theory of certain stochastic integrals. Annals of Probability 14, 840-859.
    • (1986) Annals of Probability , vol.14 , pp. 840-859
    • Stroock, D.W.1
  • 24
    • 0028426617 scopus 로고
    • Nonlinear dynamics of a shallow arch under periodic excitation, part I: 1:2 internal resonance
    • Tien, W. M., Sri Namachchivaya, N. and Bajaj, A. K. (1994a) Nonlinear dynamics of a shallow arch under periodic excitation, part I: 1:2 internal resonance. International Journal of Nonlinear Mechanics 29, 349-366.
    • (1994) International Journal of Nonlinear Mechanics , vol.29 , pp. 349-366
    • Tien, W.M.1    Sri Namachchivaya, N.2    Bajaj, A.K.3
  • 25
    • 0028424990 scopus 로고
    • Nonlinear dynamics of a shallow arch under periodic excitation, part II: 1:1 internal resonance
    • Tien, W. M., Sri Namachchivaya, N. and Malhotra, N. (1994b) Nonlinear dynamics of a shallow arch under periodic excitation, part II: 1:1 internal resonance. International Journal of Nonlinear Mechanics 29, 367-386.
    • (1994) International Journal of Nonlinear Mechanics , vol.29 , pp. 367-386
    • Tien, W.M.1    Sri Namachchivaya, N.2    Malhotra, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.