Effects of correlation time between noises on the noise enhanced stability phenomenon in an asymmetric bistable system

Abstract

The effects of the correlation time τ between noises on the noise-enhanced stability (NES) phenomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The expressions for the average escape time from the left metastable state T_L and from the right metastable state T_Rare derived. The results indicate that: i) The NES effect is suppressed as the correlation time τ increases for two metastable states; ii) The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii) In the escape process from the left state, the role of τ is opposite to that in escape from the right state.

Graphical abstract

Keywords

asymmetric bistable system / noise / correlation time / noise enhanced stability

References

[1] L. H. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys. 70(1), 223 (1998)

[2] C. R. Doering and C. J. Gadoua, Resonant activation over a fluctuating barrier, Phys. Rev. Lett.69(16), 2318 (1992)

[3] B. Spagnolo, N. Agudov, and A. Dubkov, Noise enhanced stability, Acta Phys. Pol. B35(4), 1419 (2004)

[4] J. E. Hirsch, B. A. Huberman, and D. J. Scalapino, Theory of intermittency, Phys. Rev. A25(1), 519 (1982)

[5] A. A. Dubkov, N. V. Agudov, and B. Spagnolo, Noiseenhanced stability in fluctuating metastable states, Phys. Re v . E 69(6), 061103 (2004)

[6] A. Fiasconaro, B. Spagnolo, and S. Boccaletti, Signatures of noise-enhanced stability in metastable states, Phys. Rev. E 72(6), 061110 (2005)

[7] P. D’Odorico, F. Laio, and L. Ridolfi, Noise-induced stability in dryland plant ecosystems, Proc. Natl. Acad. Sci. USA 102(31), 10819 (2005)

[8] A. Fiasconaro, B. Spagnolo, A. Ochab-Marcinek, and E. Gudowska-Nowak, Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response, Phys. Rev. E74(4), 041904 (2006)

[9] M. Yoshimoto, H. Shirahama, and S. Kurosawa, Noiseinduced order in the chaos of the Belousov–Zhabotinsky reaction, J. Chem. Phys.129(1), 014508 (2008)

[10] M. Trapanese, Noise enhanced stability in magnetic systems, J. Appl. Phys.105, 07D313 (2009)

[11] G. Z. Sun, N. Dong, G. F. Mao, J. Chen, W. W. Xu, Z. M. Ji, L. Kang, P. H. Wu, Y. Yu, and D. Y. Xing, Thermal escape from a metastable state in periodically driven Josephson junctions, Phys. Rev. E75(2), 021107 (2007)

[12] R. N. Mantegna and B. Spagnolo, Noise enhanced stability in an unstable system, Phys. Rev. Lett.76(4), 563 (1996)

[13] B. Spagnolo, A. A. Dubkov, A. L. Pankratov, E. V. Pankratova, A. Fiasconaro, and A. Ochab-Marcinek, Lifetime of metastable states and suppression of noise in interdisciplinary physical models, Acta Phys. Polo. B38(5), 1925 (2007)

[14] A. Fiasconaro and B. Spagnolo, Stability measures in metastable states with Gaussian colored noise, Phys. Rev. E80(4), 041110 (2009)

[15] A. Fiasconaro, J. J. Mazo, and B. Spagnolo, Noise-induced enhancement of stability in a metastable system with damping, Phys. Rev. E82(4), 041120 (2010)

[16] Z. L. Jia, Numerical investigation of noise enhanced stability phenomenon in a time-delayed metastable system, Chin. Phys. Lett.25(4), 1209 (2008)

[17] Z. L. Jia and D. C. Mei, Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system, J. Stat. Mech.2011(10), P10010 (2011)

[18] C. W. Xie and D. C. Mei, Mean first-passage time of a bistable kinetic model driven by multiplicative coloured noise and additive white noise, Chin. Phys. Lett. 20(6), 813 (2003)

[19] A. Mielke, Noise induced stability in fluctuating, bistable potentials, Phys. Rev. Lett. 84(5), 818 (2000)

[20] B. Dybiec and E. Gudowska-Nowak, Quantifying noise induced effects in the generic double-well potential, Acta Phys. Pol. B38(5), 1759 (2007)

[21] A. R. Bulsara, M. E. Inchiosa, and L. Gammaitoni, Noisecontrolled resonance behavior in nonlinear dynamical systems with broken symmetry, Phys. Rev. Lett. 77(11), 2162 (1996)

[22] M. E. Inchiosa, A. R. Bulsara, and L. Gammaitoni, Higherorder resonant behavior in asymmetric nonlinear stochastic systems, Phys. Rev. E55(4), 4049 (1997)

[23] S. Bouzat and H. S. Wio, Stochastic resonance in extended bistable systems: The role of potential symmetry, Phys. Rev. E59(5), 5142 (1999)

[24] L. Gammaitoni and A. R. Balsara, Noise activated nonlinear dynamic sensors, Phys. Rev. Lett. 88(23), 230601 (2002)

[25] J. H. Li, Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling, Phys. Rev. E66(3), 031104 (2002)

[26] F. Long, L. C. Du, and D. C. Mei, Asymmetric effects on the associated relaxation time and the correlation function of a bistable system with correlated noises, Phys. Scr. 79(4), 045007 (2009)

[27] D. C. Mei, Z. L. Jia, and C. J. Wang, Combined effects of asymmetry and noise correlation on the noise-enhanced stability phenomenon in a bistable system, Phys. Scr. 84(4), 045012 (2011)

[28] A. J. R. Madureira, P. P. Hänggi, and H. S. Wio, Giant suppression of the activation rate in the presence of correlated white noise sources, Phys. Lett. A217(4-5), 248 (1996)

[29] M. I. Dykman, D. G. Luchinsky, P. V. E. McClintock, N. D. Stein, and N. Stocks, Stochastic resonance for periodically modulated noise intensity, Phys. Rev. A46(4), R1713 (1992)

[30] E. A. Novikov, Functionals and the random-force method in turbulence theory, Zh. Eksp. Teor. Fiz. 47, 1919 (1964) (Sov. Phys. JETP20(5), 1290 (1965))

[31] R. F. Fox, Uniform convergence to an effective Fokker–Planck equation for weakly colored noise, Phys. Rev. A34(5), 4525 (1986)

[32] P. Hänggi, T. T. Mroczkowski, F. Moss, and P. V. E. McClintock, Bistability driven by colored noise: Theory and experiment, Phys. Rev. A32(1), 695 (1985)

[33] D. J. Wu, L. Cao, and S. Z. Ke, Bistable kinetic model driven by correlated noises: Steady-state analysis, Phys. Rev. E 50(5), 2496 (1994)

[34] D. C. Mei, G. Z. Xie, L. Cao, and D. J. Wu, Mean firstpassage time of a bistable kinetic model driven by crosscorrelated noises, Phys. Rev. E59(4), 3880 (1999)

[35] K. Lindenberg and B. J. West, The first, the biggest, and other such considerations, J. Stat. Phys. 42, 201 (1986)

[36] J. Masoliver, B. J. West, and K. Lindenbergerg, Bistability driven by Gaussian colored noise: First-passage times, Phys. Rev. A35(7), 3086 (1987)

[37] C. W. Gardiner, Handbook of Stochastic Methods, Springer Series in Synergetics, Vol. 13, Berlin: Springer-Verlag, 1983

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg