- Access by Xinjiang University
Schmitt trigger: A solvable model of stochastic resonance
Phys. Rev. E 48, 2481 – Published 1 October, 1993
DOI: https://doi.org/10.1103/PhysRevE.48.2481
Abstract
An ideal Schmitt trigger (ST) is the simplest two-state system available for realization of stochastic resonance (SR). An exact solution is found for the ST driven by exponentially correlated Gaussian noise plus a weak periodic signal. The signal-to-noise ratio is shown to pass through a maximum at a specific value of the noise intensity. A qualitative classification is given for a class of noise models which either exhibit SR or do not.
References (19)
- (a) R. Benzi, A. Sutera and A. Vulpiani, J. Phys. A 14, L453 (1981); (b) R. Benzi, G. Parisi, A. Sutera and A. Vulpiani, Tellus 34, 10 (1982); (c)SIAM J. Appl. Math. 43, 565 (1983).
- (a) C. Nicolis, Tellus 34, 1 (1982); (b) in Proceedings of the NATO ARW on Stochastic Resonance in Physics and Biology, edited by F. Moss, A. Bulsara, and M. F. Shlesinger [J. Stat. Phys. 70, 1 (1993)].
- S. Fauve and F. Heslot, Phys. Lett. 97A, 5 (1983).
- (a) B. McNamara, K. Wiesenfeld and R. Roy, Phys. Rev. Lett. 60, 2626 (1988); (b) G. Vermuri and R. Roy, Phys. Rev. A 39, 4668 (1989).
- B. McNamara and K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989).
- (a) P. Jung and P. Hänggi, Europhys. Lett. 8, 505 (1989); (b)Phys. Rev. A 41, 2977 (1990) (c)ibid. 44, 8032 (1991).
- P. Jung, Z. Phys. B 16, 521 (1989).
- T. Zhou, F. Moss and P. Jung, Phys. Rev. A 42, 3161 (1990).
- L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta and S. Santucci, Phys. Rev. Lett. 62, 349 (1989).
- H. Gang, G. Nicolis and C. Nicolis, Phys. Rev. A 42, 2030 (1990).
- I. Dayan, M. Gitterman and G. H. Weiss, Phys. Rev. A 46, 757 (1992).
- M. Dykman, P. V. E. McClintock, R. Mannella and N. Stocks, Pis'ma Zh. Eksp. Teor. Fiz. 52, 783 (1990) [JETP Lett. 52, 145 (1990)].
- L. Gammaitoni, M. Martinelli, L. Pardi and S. Santucci, Phys. Rev. Lett. 67, 1799 (1991).
- T. Zhou and F. Moss, Phys. Rev. A 41, 4255 (1990).
- (a) H. Gang, G. Qing, D. Gong and X. Weng, Phys. Rev. A 44, 6414 (1991); (b) G. De-chun, H. Gang, W. Xiao-dong, Y. Chun-yan, Q. Guang-rong, L. Rong and D. Da-fu, ibid. 46, 3243 (1992); (c) H. Gang, G. De-chun, W. Xiao-dong, Y. Chun-yuan, Q. Guang-rong and L. Rong, ibid. 46, 3250 (1992).
- Proceedings of the NATO ARW on Stochastic Resonance in Physics and Biology [Ref. 2(b)].
- Proceedings of the NATO ARW, Rate Processes in Dissipative Systems: 50 Years after Kramers, edited by P. Hänggi and J. Troe [Ber. Bunsenges. Phys. Chem. 95, (1991)].
- F. Moss, in Some Problems in Statistical Physics, edited by George Weiss, Frontiers in Applied Mathematics (SIAM, Philadelphia, in press).
- Handbook of Mathematical Functions, edited by M. Abramowitz and Irene A. Stegun (Dover, New York, 1970).