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Volumn 71, Issue 4, 2011, Pages 1458-1475

Stability of a stochastic two-dimensional non-Hamiltonian system

Author keywords

Lyapunov exponent; Markov processes; Martingale problem; Shear induced instability; Stochastic averaging

Indexed keywords

ADDITIVE WHITE NOISE; FIXED POINTS; INVARIANT MEASURE; LYAPUNOV EXPONENT; MARTINGALE PROBLEM; NOISE LIMIT; NON-HAMILTONIAN SYSTEMS; SHEAR-INDUCED INSTABILITY; STOCHASTIC AVERAGING; THIRD-ORDER; TRUNCATED NORMAL; TWO-POINT;

EID: 80052728066     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/100782139     Document Type: Article
Times cited : (26)

References (29)
  • 1
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • V. I. OSELEDEC, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc., 19(1968), pp. 197-231.
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 2
    • 0002016710 scopus 로고
    • Lyapunov exponents: A survey
    • Springer-Verlag, Berlin
    • L. ARNOLD and V. WIHSTUTZ, Lyapunov exponents: A survey, Lecture Notes in Math. 1186, Springer-Verlag, Berlin, 1986, pp. 1-26.
    • (1986) Lecture Notes in Math. , vol.1186 , pp. 1-26
    • Arnold, L.1    Wihstutz, V.2
  • 4
    • 0022737468 scopus 로고
    • Asymptotic analysis of the lyapunov exponent and rotation number of the random oscillator and applications
    • L. ARNOLD, G. PAPANICOLAOU, and V. WIHSTUTZ, Asymptotic analysis of Lyapunov exponent and rotation number of the random oscillator and applications, SIAM J. Appl. Math., 46(1986), pp. 427-450. (Pubitemid 16566013)
    • (1986) SIAM Journal on Applied Mathematics , vol.46 , Issue.3 , pp. 427-450
    • Arnold Ludwig1    Papanicolaou George2    Wihstutz Volker3
  • 5
    • 21144461048 scopus 로고
    • Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise
    • N. SRI NAMACHCHIVAYA and H. J. VAN ROESSEL, Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise, J. Statist. Phys., 71(1993), pp. 549-567.
    • (1993) J. Statist. Phys. , vol.71 , pp. 549-567
    • Sri Namachchivaya, N.1    Van Roessel, H.J.2
  • 6
    • 0003285244 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer-Verlag, New York
    • J. GUCKENHEIMER and P. HOLMES, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Appl. Math. Sci. 42, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. Sci. , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 7
    • 0014752051 scopus 로고
    • Panel flutter: A review of the aeroelastic stability of plates and shell
    • E. H. DOWELL, Panel flutter: A review of the aeroelastic stability of plates and shell, AIAA J., 8(1970), pp. 385-399.
    • (1970) AIAA J. , vol.8 , pp. 385-399
    • Dowell, E.H.1
  • 8
    • 11744276218 scopus 로고    scopus 로고
    • Dynamics of nonlinear aeroelastic systems
    • N. S. NAMACHCHIVAYA and A. LEE, Dynamics of nonlinear aeroelastic systems, Journal of Aerospace Engineering, 11(1998), pp. 59-66. (Pubitemid 128593918)
    • (1998) Journal of Aerospace Engineering , vol.11 , Issue.2 , pp. 59-66
    • Sri Namachchivaya, N.1    Lee, A.2
  • 9
    • 33749329823 scopus 로고    scopus 로고
    • Stochastic dynamics of a nonlinear aeroelastic system
    • DOI 10.2514/1.858
    • S. CHOI and N. SRI NAMACHCHIVAYA, Stochastic dynamics of a nonlinear aeroelastic system, AIAA J., 44(2006), pp. 1921-1931. (Pubitemid 44488415)
    • (2006) AIAA Journal , vol.44 , Issue.9 , pp. 1921-1931
    • Choi, S.1    Namachchivaya, N.S.2
  • 12
    • 0037376655 scopus 로고    scopus 로고
    • Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell
    • DOI 10.1016/S0955-0674(03)00017-6
    • J. J. TYSON, K. C. CHEN, and B. NOVAK, Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 15(2003), pp. 221-231. (Pubitemid 36332198)
    • (2003) Current Opinion in Cell Biology , vol.15 , Issue.2 , pp. 221-231
    • Tyson, J.J.1    Chen, K.C.2    Novak, B.3
  • 14
    • 0032494690 scopus 로고    scopus 로고
    • Bifurcation analysis of a model of mitotic control in frog eggs
    • DOI 10.1006/jtbi.1998.0781
    • M. T. BORISUK and J. J. TYSON, Bifurcation analysis of a model of mitotic control in frog eggs, J. Theoret. Biol., 195(1998), pp. 69-85. (Pubitemid 28521909)
    • (1998) Journal of Theoretical Biology , vol.195 , Issue.1 , pp. 69-85
    • Borisuk, M.T.1    Tyson, J.J.2
  • 16
    • 33645429016 scopus 로고
    • Exact stochastic simulation of coupled chemical-reactions
    • D. T. GILLESPIE, Exact stochastic simulation of coupled chemical-reactions, J. Phys. Chem., 81(1977), pp. 2340-2361.
    • (1977) J. Phys. Chem. , vol.81 , pp. 2340-2361
    • Gillespie, D.T.1
  • 17
    • 70349601544 scopus 로고    scopus 로고
    • Handbook of stochastic methods for physics
    • 3rd ed., Springer Ser. Synergetics, Springer-Verlag, Berlin
    • C. W. GARDINER, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd ed., Springer Ser. Synergetics 13, Springer-Verlag, Berlin, 2004.
    • (2004) Chemistry and the Natural Sciences , vol.13
    • Gardiner, C.W.1
  • 19
    • 4243535363 scopus 로고
    • Positive Lyapunov exponents in the Kramers oscillator
    • L. SCHIMANSKY-GEIER and H. HERZEL, Positive Lyapunov exponents in the Kramers oscillator, J. Stat. Phys., 70(1993), pp. 141-147.
    • (1993) J. Stat. Phys. , vol.70 , pp. 141-147
    • Schimansky-Geier, L.1    Herzel, H.2
  • 21
  • 22
    • 0035993030 scopus 로고    scopus 로고
    • Lyapunov exponents for small perturbations of Hamiltonian systems
    • P. H. BAXENDALE and L. GOUKASIAN, Lyapunov exponents for small perturbations of Hamiltonian systems, Ann. Probab., 30(2002), pp. 101-134.
    • (2002) Ann. Probab. , vol.30 , pp. 101-134
    • Baxendale, P.H.1    Goukasian, L.2
  • 23
    • 23044526821 scopus 로고    scopus 로고
    • On the tangent flow of a stochastic differential equation with fast drift
    • R. SOWERS, On the tangent flow of a stochastic differential equation with fast drift, Trans. Amer. Math. Soc., 353(2001), pp. 1321-1334.
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 1321-1334
    • Sowers, R.1
  • 24
    • 43049129652 scopus 로고    scopus 로고
    • Shear-induced chaos
    • K. K. LIN and L.-S. YOUNG, Shear-induced chaos, Nonlinearity, 21(2008), pp. 899-922.
    • (2008) Nonlinearity , vol.21 , pp. 899-922
    • Lin, K.K.1    Young, L.-S.2
  • 25
    • 0003203004 scopus 로고
    • Asymptotic methods in the theory of stochastic differential equations
    • Translated from the Russian by H. H. McFaden, American Mathematical Society, Providence, RI
    • A. V. SKOROKHOD, Asymptotic Methods in the Theory of Stochastic Differential Equations, Transl. Math. Monogr. 78. Translated from the Russian by H. H. McFaden, American Mathematical Society, Providence, RI, 1989.
    • (1989) Transl. Math. Monogr. , vol.78
    • Skorokhod, A.V.1
  • 26
    • 0003821975 scopus 로고
    • Dynamical systems. Differential equations, maps and chaotic behaviour
    • Chapman & Hall, London
    • D. K. ARROWSMITH and C. M. PLACE, Dynamical Systems. Differential Equations, Maps and Chaotic Behaviour, Chapman and Hall Math. Ser., Chapman & Hall, London, 1992.
    • (1992) Chapman and Hall Math. Ser.
    • Arrowsmith, D.K.1    Place, C.M.2
  • 28
    • 0004236421 scopus 로고    scopus 로고
    • Table of integrals
    • 7th ed., Elsevier/Academic Press, Amsterdam
    • I. S. GRADSHTEYN and I. M. RYZHIK, Table of Integrals, Series, and Products, 7th ed., Elsevier/Academic Press, Amsterdam, 2007.
    • (2007) Series, and Products
    • Gradshteyn, I.S.1    Ryzhik, I.M.2
  • 29
    • 4644322065 scopus 로고    scopus 로고
    • Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation
    • DOI 10.1016/j.spa.2004.05.001, PII S0304414904000833
    • P. H. BAXENDALE, Stochastic averaging and asymptotic behavior of the stochastic Duffing-van der Pol equation, Stochastic Process. Appl., 113(2004), pp. 235-272. (Pubitemid 39266093)
    • (2004) Stochastic Processes and their Applications , vol.113 , Issue.2 , pp. 235-272
    • Baxendale, P.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.