Convergence to local random attractors

Dynamical Systems

Volumn 18, Issue 2, 2003, Pages 139-158

  Ashwin, Peter ^a   Ochs, Gunter ^b  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF MOTION; LYAPUNOV METHODS; PHASE SPACE METHODS; PROBABILITY; WHITE NOISE;

DYNAMICAL SYSTEMS;

RANDOM PROCESSES;

EID: 0043032954     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/1468936031000102727     Document Type: Article

References (24)

1. Arnold, L., 1998, Random Dynamical Systems, Springer Monographs in Mathematics (Berlin: Springer Verlag).
2. Arnold, L., and Boxler, P., 1990, Stochastic bifurcation: instructive examples in dimension one. Stochastic Flows. Proceedings of Charlotte, North Carolina 1990, edited by M. Pinsky and V. Wihstutz (Basel: Birkhäuser), pp. 241-255.
3. Arnold, L., Nguyen Dinh Cong, and Oseledets, V., 1999, Jordan normal form for linear cocycles. Random Operators and Stochastic Equations, 7: 303-358.
4. Arnold, L., Sri Namachchivaya, N., and Schenk-Hoppé, K. R., 1997, Toward an understanding of stochastic Hopf bifurcation: a case study. International Journal of Bifurcation and Chaos, 6: 1947-1975.
5. Arnold, L., and Xu Kedai, 1994, Invariant measures for random dynamical systems, a necessary condition for stochastic bifurcation from a fixed point. Random and Computational Dynamics, 2: 165-182.
6. Ashwin, P., 1999a, Minimal attractors for random dynamical systems. Proceedings of the Royal Society of London A, 455: 2615-2634.
7. Ashwin, P., 1999b, Attractors of a randomly forced electronic oscillator. Physica D, 125: 302-310.
8. Ashwin, P., Buescu, J., and Stewart, I. N., 1996, From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity, 9: 703-737.
9. Baxendale, P., 1994, A stochastic Hopf bifurcation. Probability Theory and Related Fields, 99: 581-616.
10. Baxendale, P., 1999, Stability along trajectories at a stochastic bifurcation. Stochastic Dynamics (New York: Springer-Verlag), pp. 1-25.
11. Crauel, H., 1987, Random dynamical systems: positivity of Lyapunov exponents, and Markov systems. PhD thesis, University of Bremen.
12. Crauel, H., 2002a, Random Probability Measures on Polish Spaces, Stochastics Monographs Vol. 11 (London: Taylor & Francis).
13. Crauel, H., 2002b, Invariant measures for random dynamical systems on the circle. Archiv der Mathematik, 78: 145-154.
14. Crauel, H., and Flandoli, F., 1994, Attractors for random dynamical systems. Probability Theory and Related Fields, 100: 365-393.
15. Crauel, H., and Flandoli, F., 1998, Additive noise destroys a pitchfork bifurcation. Journal of Dynamics and Differential Equations, 10: 259-274.
16. Flandoli, F., and Schmalfuß, B., 1996, Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise. Stochastics and Stochastics Reports, 59: 21-45.
17. Guckenheimer, J., and Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences, 42 (New York: Springer-Verlag).
18. Keller, H., and Ochs, G., 1999, Numerical approximation of random attractors. Stochastic Dynamics, edited by H. Crauel and M. Gundlach (New York: Springer-Verlag), pp. 93-115.
19. Milnor, J., 1985, On the concept of attractor. Communications in Mathematical Physics, 99: 177-195. Comments (1985) Communications in Mathematical Physics, 102: 517-519.
20. Milnor, J., 1985, On the concept of attractor. Communications in Mathematical Physics, 99: 177-195. Comments (1985) Communications in Mathematical Physics, 102: 517-519.
21. Ochs, G., 1999, Weak random attractors, Report No. 449, Institut für Dynamische Systeme, Bremen.
22. Platt, M., Spiegel, E. A., and Tresser, C., 1993, On-off intermittency; a mechanism for bursting. Physical Review Letters, 70: 279-282.
23. Schenk-Hoppé, K. R., 1998, Random attractors - general properties, existence, and applications to stochastic bifurcation theory. Discrete and Continuous Dynamical Systems, 4: 99-130.
24. Schimansky-Geier, L., and Herzel, H., 1993, Positive Lyapunov exponents in the Kramers oscillator. Journal of Statistical Physics, 70: 141-147.