Numerical analysis of noise-induced regular oscillations

Physica D: Nonlinear Phenomena

Volumn 140, Issue 3, 2000, Pages 244-256

  Milstein, G N ^a,b   Tretyakov, M V ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b URAL FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CIRCUIT RESONANCE; DIFFERENTIAL EQUATIONS; INTEGRATION; NUMERICAL ANALYSIS; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE;

NOISE-DRIVEN SYSTEMS; STOCHASTIC RESONANCE;

CIRCUIT OSCILLATIONS;

EID: 0033732090     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00242-0     Document Type: Article

References (33)

1. R. Mannella, P.V.E. McClintock (Eds.), Proceedings of the International Workshop on Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena, Nuovo Cimento D 17 (7/8) (1995).
2. Gammaitoni L., Hänggi P., Jung P., Marchesoni F. Stochastic resonance. Rev. Mod. Phys. 70:1998;223-287.
3. Benzi R., Parisi G., Suttera A., Vulpiani A. Stochastic resonance in climatic change. Tellus. 34:1982;10-16.
4. Benzi R., Suttera A., Vulpiani A. The mechanism of stochastic resonance. J. Phys. A. 14:1981;L453-L457.
5. Nicolis C. Stochastic aspects of climatic transitions - response to a periodic forcing. Tellus. 34:1982;1-9.
6. F. Moss, Stochastic resonance: from the ice ages to the monkey's ear, in: G.H. Weiss (Ed.), Contemporary Problems in Statistical Physics, SIAM, Philadelphia, PA, 1994, pp. 205-253.
7. L. Schimansky-Geier, Th. Pöschel, Stochastic Dynamics, Lecture Notes in Physics, Vol. 484, Springer, Berlin, 1997.
8. Anishchenko V.S., Neiman A.B., Moss F., Schimansky-Geier L. Stochastic resonance: noise enhanced order. Uspechi Fizicheskich Nauk. 169:1999;7-38.
9. Dykman M.I., Mannella R., McClintock P.V.E., Stein N.D., Stocks N.G. Giant nonlinearity in the low-frequency response of a fluctuating bistable system. Phys. Rev. E. 47:1993;1629-1632.
10. Dykman M.I., Luchinsky D.G., Mannella R., McClintock P.V.E., Stein N.D., Stocks N.G. Stochastic resonance: linear response and giant nonlinearity. J. Statist. Phys. 70:1993;463-478.
11. Bartussek R., Hänggi P., Jung P. Stochastic resonance in optical bistable systems. Phys. Rev. E. 49:1994;3930-3939.
12. G.N. Milstein, M.V. Tretyakov, Regular oscillations in systems with stochastic resonance, Preprint No. 411, Weierstraß-Institut für Angewandte Analysis und Stochastic, Berlin, 1998.
13. Neiman A., Schimansky-Geier L. Stochastic resonance in two coupled bistable systems. Phys. Lett. A. 197:1995;379-386.
14. E.B. Dynkin, Markov Processes, Springer, Berlin, 1965.
15. I.I. Gichman, A.V. Skorochod, Stochastic Differential Equations, Naukova Dumka, Kiev, 1968.
16. M.I. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, NJ, 1985.
17. Milstein G.N. Solving the first boundary value problem of parabolic type by numerical integration of stochastic differential equations. Theory Probab. Appl. 40:1995;657-665.
18. G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers, Norwell, MA, 1995.
19. Milstein G.N., Tretyakov M.V. Numerical methods in the weak sense for stochastic differential equations with small noise. SIAM J. Numer. Anal. 34:1997;2142-2167.
20. Tretyakov M.V. Numerical technique for studying stochastic resonance. Phys. Rev. E. 57:1998;4789-4794.
21. Gammaitoni L., Marchesoni F., Santucci S. Stochastic resonance as a bonafide resonance. Phys. Rev. Lett. 74:1995;1052-1056.
22. Choi M.H., Fox R.F., Jung P. Quantifying stochastic resonance in bistable systems: response vs residence-time distribution functions. Phys. Rev. E. 57:1998;6335-6344.
23. Shulgin B., Neiman A., Anishchenko V. Mean switching frequency locking in stochastic bistable system driven by a periodic force. Phys. Rev. Lett. 75:1995;4157-4161.
24. Milstein G.N., Tretyakov M.V. Mean-square numerical methods for stochastic differential equations with small noises. SIAM J. Sci. Comput. 18:1997;1067-1087.
25. Lindner J.F., Meadows B.K., Ditto W.L., Inchiosa M.E., Bulsara A.R. Array enhanced stochastic resonance and spatiotemporal synchronization. Phys. Rev. Lett. 75:1995;3-6.
26. Magnasco M.O. Forced thermal ratchets. Phys. Rev. Lett. 71:1993;1477-1481.
27. P. Hänggi, R. Bartussek, Brownian rectifiers: how to covert Brownian motion into directed transport, in: J. Parisi, S.C. Müller, W. Zimmermann (Eds.), Nonlinear Physics of Complex Systems: Current Status and Future Trends, Lecture Notes in Physics, Vol. 476, Springer, Berlin, 1996, pp. 294-308.
28. Jülicher F., Ajdari A., Prost J. Modeling molecular motors. Rev. Mod. Phys. 69:1997;1269-1281.
29. Dykman M.I., Luchinsky D.G., McClintock P.V.E., Stein N.D., Stocks N.G. Stochastic resonance for periodically modulated noise intensity. Phys. Rev. A. 46:1992;R1713-R1716.
30. R.L. Stratonovich, Topics in the Theory of Random Noise, Gordon and Breach, New York, 1967.
31. W. Horsthemke, R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology, Springer, Berlin, 1984.
32. H. Risken, The Fokker-Planck Equation, Springer, Berlin, 1989.
33. Dykman M.I., Luchinsky D.G., Mannella R., McClintock P.V.E., Stein N.D., Stocks N.G. Supernarrow spectral peaks and high-frequency stochastic resonance in systems with periodic attractors. Phys. Rev. E. 49:1994;1198-1204.