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Stochastic resonance in an overdamped monostable system with multiplicative and additive α stable noise

Jiao Shang-Bin Ren Chao Li Peng-Hua Zhang Qing Xie Guo

Stochastic resonance in an overdamped monostable system with multiplicative and additive α stable noise

Jiao Shang-Bin, Ren Chao, Li Peng-Hua, Zhang Qing, Xie Guo
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  • In this paper we combine α stable noise with a monostable stochastic resonance (SR) system to investigate the overdamped monostable SR phenomenon with multiplicative and additive α stable noise, and explore the action laws of the stability index α (0 α ≤ 2) and skewness parameter β (-1 ≤ β ≤ 1) of the α stable noise, the monostable system parameter a, and the amplification factor D of the multiplicative α stable noise against the resonance output effect. Results show that for different distributions of α stable noise, the single or multiple low-and high-frequency weak signals detection can be realized by adjusting the parameter a or D within a certain range. For a or D, respectively, there is an optimal value which can make the system produce the best SR effect. Different α or β can regularly change the system resonance output effect. Moreover, when α or β is given different values, the evolution laws in the monostable SR system excited by low-and high-frequency weak signals are the same. The conclusions drawn for the study of single-and multi-frequency monostable SR with α stable noise are also the same. These results will be the foundation for realizing the adaptive parameter adjustment in the monostable SR system with α stable noise.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61304204), and the Natural Science Foundation of the Education Department of Shaanxi Province, China (Grant No. 2013JK1050).
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    [2]

    Vilar J M G, Rub J M 1996 Phys. Rev. Lett. 77 2863

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    vstigneev M, Reimann P, Pankov V, Prince R H 2004 Europhys. Lett. 65 7

    [4]

    Zhang W, Xiang B R 2006 Talanta 70 267

    [5]

    Guo F, Huang Z Q, Fan Y, Li S F, Zhang Y 2009 Chin. Phys. Lett. 26 100504

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    Zhou B C, Xu W 2009 Chaos, Solitons & Fractals 40 401

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    He C D, Xu W, Yue X L 2010 Acta Phys. Sin. 59 5276 (in Chinese)[何成娣, 徐伟, 岳晓乐2010 物理学报59 5276]

    [8]

    Zhou Y R 2011 Chin. Phys. B 20 010501

    [9]

    Li J M, Chen X F, He Z J 2011 Journal of Mechanical Engineering 47 58 (in Chinese) [李继猛, 陈雪峰, 何正嘉 2011 机械工程学报47 58]

    [10]

    Yao M L, Xu W, Ning L J 2012 Nonlinear Dyn. 67 329

    [11]

    Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese)[张晓燕, 徐伟, 周丙常2012 物理学报 61 030501]

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    Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 2712 (in Chinese)[康艳梅, 徐健学, 谢勇2003 物理学报52 2712]

    [13]

    Guo F 2009 Physica A 388 2315

    [14]

    Guo F, Luo X D, Li S F, Zhou Y R 2010 Chin. Phys. B 19 080504

    [15]

    Qiu T S, Zhang X X, Li X B, Sun Y M 2004 Statistical Signal Processing–Non-Gaussian Signal Processing and its Applications (Beijing: Publishing House of Electronics Industry) p140 (in Chinese) [邱天爽, 张旭秀, 李小兵, 孙永梅2004 统计信号处理–非高斯信号处理及其应用(北京: 电子工业出版社) 第140 页]

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    Dybiec B, Gudowska-Nowak E 2006 Acta Phys. Pol. B 37 1479

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    Zeng L Z, Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175

    [18]

    Zhang W Y, Wang Z L, Zhang W D 2009 Control Engineering of China 16 638 (in Chinese) [张文英, 王自力, 张卫东2009 控制工程16 638]

    [19]

    Zeng L Z, Xu B H 2010 Journal of physics A: Statistical Mechanics and its Applications 22 5128

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    Srokowski T 2012 Eur. Phys. J. B 85 1

    [21]

    Zhang G L, L X L, Kang Y M 2012 Acta Phys. Sin. 61 040501 (in Chinese)[张广丽, 吕希路, 康艳梅2012 物理学报61 040501]

    [22]

    Dybiec B 2009 Phys. Rev. E 80 041111

    [23]

    Hu N Q 2012 Stochastic Resonance Weak Characteristic Signal Detection Theory and Methods (Beijing: National Defense Industry Press) p60 (in Chinese) [胡茑庆2012 随机共振微弱特征信号检测理论与方法(北京: 国防工业出版社) 第60 页]

    [24]

    Jiao S B, Ren C, Huang W C, Liang Y M 2013 Acta Phys. Sin. 62 210501 (in Chinese)[焦尚彬, 任超, 黄伟超, 梁炎明2013 物理学报62 210501]

    [25]

    Tang Y, Zou W, Lu J Q, Kurths J 2012 Phys. Rev. E 85 1539

    [26]

    Liang Y J, Chen W 2013 Signal Processing 93 242

    [27]

    Agudov N V, Krichigin A V 2008 Radiophysics and Quantum Electronics 51 812

    [28]

    Weron R 1996 Statist. Prob. Lett. 28 165

    [29]

    Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502 (in Chinese)[万频, 詹宜巨, 李学聪, 王永华2011 物理学报60 040502]

    [30]

    Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese)[冷永刚, 王太勇2003 物理学报52 2432]

    [31]

    Leng Y G, Wang T Y, Qin X D, Li R X, Guo Y 2004 Acta Phys. Sin. 53 0717 (in Chinese)[冷永刚, 王太勇, 秦旭达, 李瑞欣, 郭焱2004 物理学报53 0717]

    [32]

    Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese)[冷永刚2009 物理学报58 5196]

    [33]

    Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)[林敏, 黄咏梅2006 物理学报55 3277]

    [34]

    Jiao S B, He T 2013 Computer Engineering and Applications (in Chinese) [焦尚彬, 何童2013 计算机工程与应用]

    [35]

    L Y, Wang C Y, Tian Y, Hou B 2010 China Academic Journal Electronic Publishing House 8 40 (in Chinese)[吕运, 王长悦, 田野, 侯彪2010 机械与电子8 40]

  • [1]

    Stocks N G, Stein N D, McClintock P V E 1993 J. Phys. A: Math. Gen. 26 L385

    [2]

    Vilar J M G, Rub J M 1996 Phys. Rev. Lett. 77 2863

    [3]

    vstigneev M, Reimann P, Pankov V, Prince R H 2004 Europhys. Lett. 65 7

    [4]

    Zhang W, Xiang B R 2006 Talanta 70 267

    [5]

    Guo F, Huang Z Q, Fan Y, Li S F, Zhang Y 2009 Chin. Phys. Lett. 26 100504

    [6]

    Zhou B C, Xu W 2009 Chaos, Solitons & Fractals 40 401

    [7]

    He C D, Xu W, Yue X L 2010 Acta Phys. Sin. 59 5276 (in Chinese)[何成娣, 徐伟, 岳晓乐2010 物理学报59 5276]

    [8]

    Zhou Y R 2011 Chin. Phys. B 20 010501

    [9]

    Li J M, Chen X F, He Z J 2011 Journal of Mechanical Engineering 47 58 (in Chinese) [李继猛, 陈雪峰, 何正嘉 2011 机械工程学报47 58]

    [10]

    Yao M L, Xu W, Ning L J 2012 Nonlinear Dyn. 67 329

    [11]

    Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese)[张晓燕, 徐伟, 周丙常2012 物理学报 61 030501]

    [12]

    Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 2712 (in Chinese)[康艳梅, 徐健学, 谢勇2003 物理学报52 2712]

    [13]

    Guo F 2009 Physica A 388 2315

    [14]

    Guo F, Luo X D, Li S F, Zhou Y R 2010 Chin. Phys. B 19 080504

    [15]

    Qiu T S, Zhang X X, Li X B, Sun Y M 2004 Statistical Signal Processing–Non-Gaussian Signal Processing and its Applications (Beijing: Publishing House of Electronics Industry) p140 (in Chinese) [邱天爽, 张旭秀, 李小兵, 孙永梅2004 统计信号处理–非高斯信号处理及其应用(北京: 电子工业出版社) 第140 页]

    [16]

    Dybiec B, Gudowska-Nowak E 2006 Acta Phys. Pol. B 37 1479

    [17]

    Zeng L Z, Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175

    [18]

    Zhang W Y, Wang Z L, Zhang W D 2009 Control Engineering of China 16 638 (in Chinese) [张文英, 王自力, 张卫东2009 控制工程16 638]

    [19]

    Zeng L Z, Xu B H 2010 Journal of physics A: Statistical Mechanics and its Applications 22 5128

    [20]

    Srokowski T 2012 Eur. Phys. J. B 85 1

    [21]

    Zhang G L, L X L, Kang Y M 2012 Acta Phys. Sin. 61 040501 (in Chinese)[张广丽, 吕希路, 康艳梅2012 物理学报61 040501]

    [22]

    Dybiec B 2009 Phys. Rev. E 80 041111

    [23]

    Hu N Q 2012 Stochastic Resonance Weak Characteristic Signal Detection Theory and Methods (Beijing: National Defense Industry Press) p60 (in Chinese) [胡茑庆2012 随机共振微弱特征信号检测理论与方法(北京: 国防工业出版社) 第60 页]

    [24]

    Jiao S B, Ren C, Huang W C, Liang Y M 2013 Acta Phys. Sin. 62 210501 (in Chinese)[焦尚彬, 任超, 黄伟超, 梁炎明2013 物理学报62 210501]

    [25]

    Tang Y, Zou W, Lu J Q, Kurths J 2012 Phys. Rev. E 85 1539

    [26]

    Liang Y J, Chen W 2013 Signal Processing 93 242

    [27]

    Agudov N V, Krichigin A V 2008 Radiophysics and Quantum Electronics 51 812

    [28]

    Weron R 1996 Statist. Prob. Lett. 28 165

    [29]

    Wan P, Zhan Y J, Li X C, Wang Y H 2011 Acta Phys. Sin. 60 040502 (in Chinese)[万频, 詹宜巨, 李学聪, 王永华2011 物理学报60 040502]

    [30]

    Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese)[冷永刚, 王太勇2003 物理学报52 2432]

    [31]

    Leng Y G, Wang T Y, Qin X D, Li R X, Guo Y 2004 Acta Phys. Sin. 53 0717 (in Chinese)[冷永刚, 王太勇, 秦旭达, 李瑞欣, 郭焱2004 物理学报53 0717]

    [32]

    Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese)[冷永刚2009 物理学报58 5196]

    [33]

    Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)[林敏, 黄咏梅2006 物理学报55 3277]

    [34]

    Jiao S B, He T 2013 Computer Engineering and Applications (in Chinese) [焦尚彬, 何童2013 计算机工程与应用]

    [35]

    L Y, Wang C Y, Tian Y, Hou B 2010 China Academic Journal Electronic Publishing House 8 40 (in Chinese)[吕运, 王长悦, 田野, 侯彪2010 机械与电子8 40]

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  • Received Date:  22 November 2013
  • Accepted Date:  25 December 2013
  • Published Online:  05 April 2014

Stochastic resonance in an overdamped monostable system with multiplicative and additive α stable noise

  • 1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 61304204), and the Natural Science Foundation of the Education Department of Shaanxi Province, China (Grant No. 2013JK1050).

Abstract: In this paper we combine α stable noise with a monostable stochastic resonance (SR) system to investigate the overdamped monostable SR phenomenon with multiplicative and additive α stable noise, and explore the action laws of the stability index α (0 α ≤ 2) and skewness parameter β (-1 ≤ β ≤ 1) of the α stable noise, the monostable system parameter a, and the amplification factor D of the multiplicative α stable noise against the resonance output effect. Results show that for different distributions of α stable noise, the single or multiple low-and high-frequency weak signals detection can be realized by adjusting the parameter a or D within a certain range. For a or D, respectively, there is an optimal value which can make the system produce the best SR effect. Different α or β can regularly change the system resonance output effect. Moreover, when α or β is given different values, the evolution laws in the monostable SR system excited by low-and high-frequency weak signals are the same. The conclusions drawn for the study of single-and multi-frequency monostable SR with α stable noise are also the same. These results will be the foundation for realizing the adaptive parameter adjustment in the monostable SR system with α stable noise.

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