Additive noise destroys a pitchfork bifurcation

Journal of Dynamics and Differential Equations

Volumn 10, Issue 2, 1998, Pages 259-274

  Crauel, Hans ^a   Flandoli, Franco ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b Dipartimento di Matematica Applicata U Dini   (Italy)

Author keywords

Invariant measures; Markov measures; Random attractors; Random dynamical systems

Indexed keywords

EID: 54649084055     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1022665916629     Document Type: Article

References (16)

1. Arnold, L. (1998). Random Dynamical Systems, Springer, Berlin.
2. Arnold, L., and Boxler, P. (1992). Stochastic bifurcation: Instructive examples in dimension one. In Pinsky, M. A., and Wihstutz, V. (eds.), Diffusion Processes and Related Problems in Analysis, Vol. II. Stochastic Flows, Birkhäuser, Boston, pp. 241-255.
3. Arnold, L., and Crauel, H. (1991). Random dynamical systems. In Arnold, L., Crauel, H., and Eckmann, J. P. (eds.), Lyapunov Exponents, Proceedings, Oberwolfach 1990, Lecture Notes in Mathematics 1486, Springer, Berlin, pp. 1-22.
4. Arnold, L., and Scheutzow, M. (1995). Perfect cocycles through stochastic differential equations. Prob. Theory Relat. Fields 101, 65-88.
5. Baxendale, P. H. (1994). A stochastic Hopf bifurcation. Prob. Theory Relat. Fields 99, 581-616.
6. Castaing, C., and Valadier, M. (1977). Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer, Berlin.
7. Crauel, H. (1990). Extremal exponents of random dynamical systems do not vanish. J. Dynam. Diff. Eq. 2, 245-291.
8. Crauel, H. (1991). Markov measures for random dynamical systems. Stochast. Stochast. Rep. 37, 153-173.
9. Crauel, H. (1995). Random Probability Measures on Polish Spaces, Habilitationsschrift, Bremen.
10. Crauel, H. (1998). Global random attractors are uniquely determined by attracting deterministic compact sets, to appear in Annali di Matematica.
11. Crauel, H., Debussche, A., and Flandoli, F. (1995). Random attractors. J. Dynam. Diff. Eqs. 9, 307-341.
12. Crauel, H., and Flandoli, F. (1994). Attractors for random dynamical systems. Prob. Theory Relat. Fields 100, 365-393.
13. Has'minskiǐ, R. Z. (1980). Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, Aalphen aan de Rijn.
14. Horsthemke, W., and Lefever, R. (1984). Noise-Induced Transitions, Theory and Applications in Physics, Chemistry and Biology, Springer, Berlin.
15. Ichihara, K., and Kunita, H. (1974). A classification of the second order degenerate elliptic operators and its probabilistic characterization. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 30, 235-254, (1977). 39, 81-84 (supplements).
16. Temam, R. (1988). Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York.