Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

doi:10.1088/1674-1056/27/5/050501

Abstract Stochastic resonance (SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory (LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density (PSD) and signal-to-noise ratio (SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.

Keywords: stochastic resonance under-damped bistable system spectral amplification harmonic mixing signal

Received: 05 January 2018
Revised: 09 February 2018
Accepted manuscript online:

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

Fund: Project supported by the National Natural Science Foundation of China (Grant No.11772048).

Corresponding Authors: Yan-Fei Jin
E-mail: jinyf@bit.edu.cn

Cite this article:

Yan-Fei Jin(靳艳飞) Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal 2018 Chin. Phys. B 27 050501

[13]	Yang J H and Liu X B 2010 Chaos 20 033124
[1]	Gammaitoni L, Hänggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[14]	Yang J H, Sanjuán M A F and Liu H G 2016 Commun. Nonlinear Sci. Numer. Simulat. 30 362
[2]	McNamara B and Wiesenfeld K 1989 Phys Rev A 39 4854
[15]	Gammaitoni L, Löcher M, Bulsara A, Hänggi P, Neff J, Wisesnfeld K, Ditto W and Inchiosa M E 1999 Phys. Rev. Lett. 82 4574
[3]	Hu G, Nicolis G and Nicolis C 1990 Phys. Rev. A 42 2030
[16]	Löcher M, Inchiosa M E, Neff J, Bulsara A, Wiesenfeld K, Gammaitoni L, Hänggi P and Ditto W 2000 Phys. Rev. E 62 317
[4]	Xu Y, Wu J, Du L and Yang H 2016 Chaos Solit. Fract. 92 91
[17]	Schmid G and Hänggi P 2005 Physica A 351 95
[5]	Jin Y F, Ma Z M and Xiao S M 2017 Chaos Solit. Fract. 103 470
[18]	Grigorenko A N, Nikitin P I and Roschepkin G V 1996 J. Appl. Phys. 79 6113
[6]	Xu P F, Jin Y F and Xiao S M 2017 Chaos 27 113109
[19]	Jin Y F, Xu W and Xu M 2005 Chin. Phys. Lett. 22 1061
[7]	Ai B Q and Liu L G 2007 J. Stat. Mech. 2007 P02019
[20]	Machura L, Kostur M and Luczka J 2010 Chem. Phys. 375 445
[8]	Landa P S and Mcclintock P V E 2000 J. Phys. A 33 L433
[21]	Du L C and Mei D C 2011 Physica A 390 3262
[9]	Gitterman M 2001 J. Phys. A 34 L355
[22]	Wu J and Xu Y 2014 Discrete Dyn. Nat. Soc. 2014 850361
[10]	Jung P and Talkner P 1995 Phys. Rev. E 51 2640
[23]	Saikia S 2014 Physica A 416 411
[11]	Chizhevsky V N 2015 Phys. Rev. E 92 032902
[24]	Hennig D, Schimansky-Geier L and Hänggi P 2009 Phys. Rev. E 79 041117
[12]	Chizhevsky V N 2014 Phys. Rev. E 90 042924
[25]	Lindner B, Schimansky-Geier L, Reimann P, Hänggi P and Nagaoka M 1999 Phys. Rev. E 59 1417
[13]	Yang J H and Liu X B 2010 Chaos 20 033124
[26]	Kang Y M, Xu J X and Xie Y 2003 Acta Phys. Sin. 52 802(in Chinese)
[14]	Yang J H, Sanjuán M A F and Liu H G 2016 Commun. Nonlinear Sci. Numer. Simulat. 30 362
[27]	Kang Y M, Xu J X and Xie Y 2003 Phys. Rev. E 68 036123
[15]	Gammaitoni L, Löcher M, Bulsara A, Hänggi P, Neff J, Wisesnfeld K, Ditto W and Inchiosa M E 1999 Phys. Rev. Lett. 82 4574
[28]	Xiao S M and Jin Y F 2017 Nonlinear Dyn. 90 2069
[16]	Löcher M, Inchiosa M E, Neff J, Bulsara A, Wiesenfeld K, Gammaitoni L, Hänggi P and Ditto W 2000 Phys. Rev. E 62 317
[29]	Liu K H and Jin Y F 2013 Physica A 392 5283
[17]	Schmid G and Hänggi P 2005 Physica A 351 95
[30]	Jin Y F, Xie W X and Liu K H 2017 Procedia IUTAM 22 267
[18]	Grigorenko A N, Nikitin P I and Roschepkin G V 1996 J. Appl. Phys. 79 6113
[31]	Xu Y, Wu J, Zhang H Q and Ma S J 2012 Nonlinear Dyn. 70 531
[19]	Jin Y F, Xu W and Xu M 2005 Chin. Phys. Lett. 22 1061
[20]	Machura L, Kostur M and Luczka J 2010 Chem. Phys. 375 445
[21]	Du L C and Mei D C 2011 Physica A 390 3262
[22]	Wu J and Xu Y 2014 Discrete Dyn. Nat. Soc. 2014 850361
[23]	Saikia S 2014 Physica A 416 411
[24]	Hennig D, Schimansky-Geier L and Hänggi P 2009 Phys. Rev. E 79 041117
[25]	Lindner B, Schimansky-Geier L, Reimann P, Hänggi P and Nagaoka M 1999 Phys. Rev. E 59 1417
[26]	Kang Y M, Xu J X and Xie Y 2003 Acta Phys. Sin. 52 802(in Chinese)
[27]	Kang Y M, Xu J X and Xie Y 2003 Phys. Rev. E 68 036123
[28]	Xiao S M and Jin Y F 2017 Nonlinear Dyn. 90 2069
[29]	Liu K H and Jin Y F 2013 Physica A 392 5283
[30]	Jin Y F, Xie W X and Liu K H 2017 Procedia IUTAM 22 267
[31]	Xu Y, Wu J, Zhang H Q and Ma S J 2012 Nonlinear Dyn. 70 531

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Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

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