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Effect of non-Gaussian noise sources in a noise-induced transition. (English) Zbl 1062.82048

Summary: Here we study a noise-induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show – using both, a theoretical approximation and numerical simulations – that there is a shift of the transition as the noise departs from the Gaussian behavior. Also, we confirm the reentrance effect found for colored Gaussian noise and show the behavior of the transition line in the phase-like diagram as the noise departs from Gaussianity in the large correlation time limit.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics

References:

[1] Gammaitoni, L.; Hänggi, P.; Jung, P.; Marchesoni, F., Rev. Mod. Phys., 70, 223 (1998)
[2] Lindner, J. F.; Meadows, B. K.; Ditto, W. L.; Inchiosa, M. E.; Bulsara, A., Phys. Rev. E, 53, 2081 (1996)
[3] Wio, H. S.; Von Haeften, B.; Bouzat, S., Physica A, 306C, 140 (2002) · Zbl 0994.82060
[4] W. Horsthemke, R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology, Springer, Berlin, 1984.; W. Horsthemke, R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology, Springer, Berlin, 1984. · Zbl 0529.60085
[5] Van den Broeck, C.; Parrondo, J. M.R.; Toral, R.; Kawai, R., Phys. Rev. E, 55, 4084 (1997)
[6] Mangioni, S.; Deza, R.; Toral, R.; Wio, H. S., Phys. Rev. E, 61, 223 (2000)
[7] Reimann, P., Phys. Rep., 361, 57 (2002) · Zbl 1001.82097
[8] Astumian, R. D.; Hänggi, P., Phys. Today, 55, 11, 33 (2002)
[9] Reimann, P.; Kawai, R.; Van den Broeck, C.; Hänggi, P., Europhys. Lett., 45, 545 (1999)
[10] Mangioni, S.; Deza, R.; Wio, H. S., Phys. Rev. E, 63, 041115 (2001)
[11] J. Garcı́a-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems, Springer-Verlag, New York, 1999.; J. Garcı́a-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems, Springer-Verlag, New York, 1999. · Zbl 0938.60002
[12] A. Manwani, PhD Thesis, CALTECH, 2000.; A. Manwani, PhD Thesis, CALTECH, 2000.
[13] Van den Broeck, C.; Hänggi, P., Phys. Rev. A, 30, 2730 (1984)
[14] Soldatov, A. V., Mod. Phys. Lett. B, 7, 1253 (1993)
[15] Castro, F.; Sánchez, A.; Wio, H. S., Phys. Rev. Lett., 75, 1691 (1995)
[16] Borland, L., Phys. Lett. A, 245, 67 (1998) · Zbl 0940.82049
[17] Tsallis, C., Phys. World, 10, 42 (1997) · Zbl 0904.90019
[18] M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy—Interdisciplinary Applications, Oxford University Press, Oxford, 2003.; M. Gell-Mann, C. Tsallis (Eds.), Nonextensive Entropy—Interdisciplinary Applications, Oxford University Press, Oxford, 2003.
[19] H.S. Wio, On the Role of Non-Gaussian Noises in Noise Induced Phenomena, Chapter in Ref. [18]; H.S. Wio, On the Role of Non-Gaussian Noises in Noise Induced Phenomena, Chapter in Ref. [18]
[20] Fuentes, M. A.; Wio, H. S.; Toral, R., Physica A, 303, 91 (2002) · Zbl 0979.82051
[21] Hänggi, P., Chem. Phys., 180, 157 (1994)
[22] Fuentes, M. A.; Toral, R.; Wio, H. S., Physica A, 295, 114 (2001) · Zbl 0978.60056
[23] Castro, F. J.; Kuperman, M. N.; Fuentes, M. A.; Wio, H. S., Phys. Rev. E, 64, 051105 (2001)
[24] H.S. Wio, Application of path integration to stochastic processes: an introduction, in: G. Zgrablich (Ed.), Fundamentals and Applications of Complex Systems, Nueva Ed. Univ., U.N. San Luis, 1999, p. 253.; H.S. Wio, Application of path integration to stochastic processes: an introduction, in: G. Zgrablich (Ed.), Fundamentals and Applications of Complex Systems, Nueva Ed. Univ., U.N. San Luis, 1999, p. 253.
[25] Wio, H. S.; Revelli, J. A.; Sánchez, A. D., Physica D, 168-169, 165 (2002) · Zbl 1002.92007
[26] S. Bouzat, H.S. Wio, Strong enhancement of current, efficiency and mass separation in Brownian motors driven by non-Gaussian noises. cond-mat/0112304; S. Bouzat, H.S. Wio, Strong enhancement of current, efficiency and mass separation in Brownian motors driven by non-Gaussian noises. cond-mat/0112304
[27] M. San Miguel, R. Toral, Stochastic effects in physical systems, in: E. Tirapegui, J. Martínez, R. Tiemann (Eds.), Instabilities and Nonequilibrium Structures VI, Kluwer Academic Publishers, Dordrecht, 1999, pp. 35-130.; M. San Miguel, R. Toral, Stochastic effects in physical systems, in: E. Tirapegui, J. Martínez, R. Tiemann (Eds.), Instabilities and Nonequilibrium Structures VI, Kluwer Academic Publishers, Dordrecht, 1999, pp. 35-130.
[28] Toral, R.; Chakrabarti, A., Comput. Phys. Commun., 74, 327 (1993) · Zbl 0854.65005
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