Stochastic resonance in an over-damped linear oscillator

doi:10.1088/1674-1056/23/8/080503

Abstract For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance (SR) in this paper. Using the Shapiro-Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio (SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.

Keywords: stochastic resonance signal-to-noise ratio periodically modulated noise cross-correlation intensity between noises

Received: 18 December 2013
Revised: 18 February 2014
Accepted manuscript online:

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.40.Ca	(Noise)
	02.50.-r	(Probability theory, stochastic processes, and statistics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171238), the Young Teacher Fund of Fujian Agriculture and Forestry Uninversity, China (Grant No. 2011XJJ23), and the Science and Technology Project of the Education Department of Sichuan Province, China (Grant No. 14ZA0050).

Corresponding Authors: Ma Hong
E-mail: mahong@scu.edu.cn

Cite this article:

Lin Li-Feng (林丽烽), Tian Yan (田艳), Ma Hong (马洪) Stochastic resonance in an over-damped linear oscillator 2014 Chin. Phys. B 23 080503

[1]	Benzi R, Sutera A and Vulpliani A 1981 J. Phys. A: Math. Gen. 14 L453
[2]	Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[3]	Gitterman M 2003 Phys. Rev. E 67 057103
[4]	Jia Y, Yu S N and Li J R 2000 Phys. Rev. E 62 1869
[5]	Luo X Q and Zhu S Q 2003 Phys. Rev. E 67 021104
[6]	Katrin L, Romi M and Astrid R 2009 Phys. Rev. E 79 051128
[7]	Li D S and Li J H 2010 Commun. Theor. Phys. 53 298
[8]	Jin Y F and Hu H Y 2009 Acta Phys. Sin. 58 2895 (in Chinese)
[9]	Xu W, Jin Y F, Xu M and Li W 2005 Acta Phys. Sin. 54 5027 (in Chinese)
[10]	Zhou B C and Xu W 2007 Acta Phys. Sin. 56 5623 (in Chinese)
[11]	Zhang L Y, Jin G X and Chao L 2011 Acta Phys. Sin. 60 044207 (in Chinese)
[12]	Tu Z, Peng H, Wang F and Ma H 2013 Acta Phys. Sin. 62 030502 (in Chinese)
[13]	Fulinski A and Telejko T 1991 Phys. Lett. A 152 11
[14]	Zhou B C and Xu W 2008 Acta Phys. Sin. 57 2035 (in Chinese)
[15]	Zhang L, Zhong S C, Peng H and Luo M K 2012 Acta Phys. Sin. 61 130503 (in Chinese)
[16]	Tian Y, Huang L and Luo M K 2013 Acta Phys. Sin. 62 050502 (in Chinese)
[17]	Chen D Y and Wang Z L 2009 Acta Phys. Sin. 58 1403 (in Chinese)
[18]	Chen D Y and Zhang L 2009 Chin. Phys. B 18 1755
[19]	Tessone C J and Wio H S 1998 Mod. Phys. Lett. B 12 1195
[20]	Tessone C J, Wio H S and Hanggi P 2000 Phys. Rev. E 62 4623
[21]	Gammaitoni L, Marchesoni F and Santucci S 1995 Phys. Rev. Lett. 74 1052
[22]	Shapiro V E and Loginov V M 1978 Physica A 91 563
[23]	Fulinski A 1995 Phys. Rev. E 52 4523
[24]	Gardiner C W 1983 Handbook of Stochastic Processes (Berlin: Springer) p. 86

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