메뉴 건너뛰기




Volumn 11, Issue 3, 1996, Pages 255-274

Bifurcation scenarios of the noisy Duffing-van der Pol oscillator

Author keywords

Duffing van der Pol oscillator; Invariant measures; Lyapunov exponents; Random dynamical systems; Stochastic bifurcation; Stochastic numerics

Indexed keywords

BIFURCATION (MATHEMATICS); INVARIANCE; LYAPUNOV METHODS; NUMERICAL ANALYSIS; RANDOM PROCESSES; STABILITY;

EID: 0030290070     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf00120720     Document Type: Article
Times cited : (121)

References (31)
  • 2
    • 0039950361 scopus 로고
    • Six lectures on random dynamical systems (CIME Summer School)
    • Springer-Verlag, Berlin
    • Arnold, L., 'Six lectures on random dynamical systems (CIME Summer School)', in Lecture Notes in Mathematics, Vol. 1609, Springer-Verlag, Berlin, 1995, pp.1-43.
    • (1995) Lecture Notes in Mathematics , vol.1609 , pp. 1-43
    • Arnold, L.1
  • 3
    • 0004162673 scopus 로고
    • Stochastic bifurcation: Instructive examples in dimension one
    • M. Pinsky and V. Wihstutz (eds.), Birkhäuser, Boston
    • Arnold, L. and Boxler, P., 'Stochastic bifurcation: Instructive examples in dimension one', in Progress in Probability, Vol. 27, M. Pinsky and V. Wihstutz (eds.), Birkhäuser, Boston, 1992, pp. 241-256.
    • (1992) Progress in Probability , vol.27 , pp. 241-256
    • Arnold, L.1    Boxler, P.2
  • 4
    • 0002155244 scopus 로고
    • Random dynamical systems
    • Springer-Verlag, Berlin
    • Arnold, L. and Crauel, H., 'Random dynamical systems', in Lecture Notes in Mathematics, Vol. 1486, Springer-Verlag, Berlin, 1991, pp. 1-22.
    • (1991) Lecture Notes in Mathematics , vol.1486 , pp. 1-22
    • Arnold, L.1    Crauel, H.2
  • 5
    • 21844488246 scopus 로고
    • Perfect cocycles through stochastic differential equations
    • Arnold, L. and Scheutzow, M., 'Perfect cocycles through stochastic differential equations', Probability Theory and Related Fields 101, 1995, 65-88.
    • (1995) Probability Theory and Related Fields , vol.101 , pp. 65-88
    • Arnold, L.1    Scheutzow, M.2
  • 8
    • 0011680282 scopus 로고
    • Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point
    • Arnold, L. and Xu Kedai, 'Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point', Random & Computational Dynamics 2, 1994, 165-182.
    • (1994) Random & Computational Dynamics , vol.2 , pp. 165-182
    • Arnold, L.1    Kedai, X.2
  • 10
    • 0003194069 scopus 로고
    • Asymptotic behaviour of stochastic flows of diffeomorphisms
    • Springer-Verlag, Berlin
    • Baxendale, P. H., 'Asymptotic behaviour of stochastic flows of diffeomorphisms', in Lecture Notes in Mathematics, Vol. 1203, Springer-Verlag, Berlin, 1986, pp. 1-19.
    • (1986) Lecture Notes in Mathematics , vol.1203 , pp. 1-19
    • Baxendale, P.H.1
  • 11
    • 0001846760 scopus 로고
    • Stability and equilibrium properties of stochastic flows of diffeomorphisms
    • M. Pinsky and V. Wihstutz (eds.), Birkhäuser, Boston
    • Baxendale, P. H., 'Stability and equilibrium properties of stochastic flows of diffeomorphisms', in Progress in Probability, Vol. 27, M. Pinsky and V. Wihstutz (eds.), Birkhäuser, Boston, 1992, pp. 3-35.
    • (1992) Progress in Probability , vol.27 , pp. 3-35
    • Baxendale, P.H.1
  • 12
    • 0028419946 scopus 로고
    • Random perturbations of bifurcation diagrams
    • Colonius, F. and Kliemann, W., 'Random perturbations of bifurcation diagrams', Nonlinear Dynamics 5, 1994, 353-373.
    • (1994) Nonlinear Dynamics , vol.5 , pp. 353-373
    • Colonius, F.1    Kliemann, W.2
  • 13
    • 0001516826 scopus 로고
    • Extremal exponents of random dynamical systems do not vanish
    • Crauel, H., 'Extremal exponents of random dynamical systems do not vanish', Dynamics and Differential Equations 2, 1990, 245-291.
    • (1990) Dynamics and Differential Equations , vol.2 , pp. 245-291
    • Crauel, H.1
  • 24
    • 0000438813 scopus 로고
    • Lyapunov exponents and rotation number of two dimensional linear stochastic systems with small diffusions
    • Pardoux, E. and Wihstutz, V., 'Lyapunov exponents and rotation number of two dimensional linear stochastic systems with small diffusions ', SIAM Journal on Applied Mathematics 48, 1988, 442-457.
    • (1988) SIAM Journal on Applied Mathematics , vol.48 , pp. 442-457
    • Pardoux, E.1    Wihstutz, V.2
  • 26
    • 0030487210 scopus 로고    scopus 로고
    • Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive
    • Schenk-Hoppé, K. R., 'Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive', ZAMP - Journal of Applied Mathematics and Physics 47, 1996, 1-20.
    • (1996) ZAMP - Journal of Applied Mathematics and Physics , vol.47 , pp. 1-20
    • Schenk-Hoppé, K.R.1
  • 28
    • 0003908257 scopus 로고
    • Measure attractors and stochastic attractors
    • Universität Bremen
    • Schmalfuß, B., 'Measure attractors and stochastic attractors', Technical Report No. 332, Universität Bremen, 1995.
    • (1995) Technical Report No. 332 , vol.332
    • Schmalfuß, B.1
  • 30
    • 0026118691 scopus 로고
    • Co-dimension two bifurcations in the presence of noise
    • Sri Namachchivaya, N., 'Co-dimension two bifurcations in the presence of noise', Journal of Applied Mechanics 58, 1991, 259-265.
    • (1991) Journal of Applied Mechanics , vol.58 , pp. 259-265
    • Sri Namachchivaya, N.1
  • 31
    • 0003208202 scopus 로고
    • Simulation and numerical analysis of stochastic differential systems: A review
    • Springer-Verlag, Berlin
    • Talay, D., 'Simulation and numerical analysis of stochastic differential systems: A review', in Lecture Notes in Physics, Vol. 451, Springer-Verlag, Berlin, 1995, pp. 54-96.
    • (1995) Lecture Notes in Physics , vol.451 , pp. 54-96
    • Talay, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.