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Volumn 31, Issue 5 SPEC. ISS., 1996, Pages 685-692

Stochastic Hopf bifurcation: An example

(1)  Schenk Hoppe K R a  

a NONE

Author keywords

Invariant measures; Lyapunov exponents; Random dynamical systems; Stochastic Hopf bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); DYNAMICS; INVARIANCE; LYAPUNOV METHODS; NONLINEAR EQUATIONS; NUMERICAL METHODS; RANDOM PROCESSES; SYSTEM STABILITY;

EID: 0030241802     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7462(96)00030-3     Document Type: Article
Times cited : (22)

References (21)
  • 2
    • 0022524005 scopus 로고
    • Influence of noise on duffing-van der pol oscillators
    • W. Ebeling, H. Herzel, W. Richert and L. Schimansky-Geier, Influence of noise on Duffing-van der Pol oscillators. ZAMM 66(3), 141 (1986).
    • (1986) ZAMM , vol.66 , Issue.3 , pp. 141
    • Ebeling, W.1    Herzel, H.2    Richert, W.3    Schimansky-Geier, L.4
  • 3
    • 0026118691 scopus 로고
    • Co-dimension two bifurcations in the presence of noise
    • N. Sri Namachchivaya, Co-dimension two bifurcations in the presence of noise. J. Appl. Mech. 58, 259 (1991).
    • (1991) J. Appl. Mech. , vol.58 , pp. 259
    • Namachchivaya, N.S.1
  • 7
    • 0011680282 scopus 로고
    • Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point
    • L. Arnold and Xu Kedai, Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Rand. Comput. Dyn. 2, 165 (1994).
    • (1994) Rand. Comput. Dyn. , vol.2 , pp. 165
    • Arnold, L.1    Kedai, X.2
  • 8
    • 21844497123 scopus 로고
    • A stochastic hopf bifurcation
    • P. H. Baxendale, A stochastic Hopf bifurcation. Prob. Th. Rel. Fields 99, 581 (1994).
    • (1994) Prob. Th. Rel. Fields , vol.99 , pp. 581
    • Baxendale, P.H.1
  • 9
    • 0030290070 scopus 로고    scopus 로고
    • Bifurcation scenarios of the noisy Duffing-van der pol oscillator
    • to appear
    • K. R. Schenk-Hoppé, Bifurcation scenarios of the noisy Duffing-van der Pol oscillator. Nonlinear Dynamics (to appear) (1996).
    • (1996) Nonlinear Dynamics
    • Schenk-Hoppé, K.R.1
  • 12
    • 0000124397 scopus 로고
    • Expansion of the global error for numerical schemes solving SDE
    • D. Talay and L. Tubaro, Expansion of the global error for numerical schemes solving SDE. Stoch. Anal. Applic. 8(4), 483 (1990).
    • (1990) Stoch. Anal. Applic. , vol.8 , Issue.4 , pp. 483
    • Talay, D.1    Tubaro, L.2
  • 14
    • 21844488246 scopus 로고
    • Perfect cocycles through stochastic differential equations
    • L. Arnold and M. Scheutzow, Perfect cocycles through stochastic differential equations. Probab. Th. Rel. Fields 101, 65 (1995).
    • (1995) Probab. Th. Rel. Fields , vol.101 , pp. 65
    • Arnold, L.1    Scheutzow, M.2
  • 15
    • 0030487210 scopus 로고    scopus 로고
    • Deterministic and stochastic duffing-van der pol oscillators are non-explosive
    • to appear
    • K. R. Schenk-Hoppé, Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive. ZAMP J. Appl. Math. Physics (to appear) (1996).
    • (1996) ZAMP J. Appl. Math. Physics
    • Schenk-Hoppé, K.R.1
  • 16
    • 0001516826 scopus 로고
    • Extremal exponents of random dynamical systems do not vanish
    • H. Crauel, Extremal exponents of random dynamical systems do not vanish. Dynamics Differ. Equations 2, 245 (1990).
    • (1990) Dynamics Differ. Equations , vol.2 , pp. 245
    • Crauel, H.1
  • 17
    • 21844482698 scopus 로고
    • Attractors for random dynamical systems
    • H. Crauel and F. Flandoli, Attractors for random dynamical systems. Probab. Th. Rel. Fields 100, 365 (1994).
    • (1994) Probab. Th. Rel. Fields , vol.100 , pp. 365
    • Crauel, H.1    Flandoli, F.2
  • 18
    • 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 the Lyapunov exponent and rotation number of the random oscillator and applications. SIAM J. Appl. Math. 46, 427 (1986).
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 427
    • Arnold, L.1    Papanicolaou, G.2    Wihstutz, V.3
  • 19
    • 0024135650 scopus 로고
    • Hopf bifurcation in the presence of both parametric and external stochastic excitations
    • N. Sri Namachchivaya, Hopf bifurcation in the presence of both parametric and external stochastic excitations. J. Appl. Mech. 110, 923 (1988).
    • (1988) J. Appl. Mech. , vol.110 , pp. 923
    • Sri Namachchivaya, N.1
  • 21
    • 0000515929 scopus 로고
    • Lyapunov exponent of linear stochastic systems with large diffusion term
    • E. Pardoux and V. Wihstutz, Lyapunov exponent of linear stochastic systems with large diffusion term. Stoch. Process. Appl. 40, 289 (1992).
    • (1992) Stoch. Process. Appl. , vol.40 , pp. 289
    • Pardoux, E.1    Wihstutz, V.2


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