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Parameter-induced stochastic resonance in overdamped system with stable noise

Zhang Guang-Li Lü Xi-Lu Kang Yan-Mei

Parameter-induced stochastic resonance in overdamped system with stable noise

Zhang Guang-Li, Lü Xi-Lu, Kang Yan-Mei
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  • Parameter-induced stochastic resonance is an important method of detecting weak signal from noise, but under stable noise background, this method has not been reported. In this paper, we study the parameter-induced stochastic resonance in an overdamped system with stable noise. Our investigation discloses that the stochastic resonance can be realized by tuning the system parameter under stable noise background; when the nonlinear term parameter is turned, the resonant effect becomes weakened as the stability index decreases. But when the linear term parameter is turned, the resonant effect becomes strengthened as the stability index decreases. Our observation is significant for understanding the positive role of stable noise in weak signal detection, which is helpful for understanding the effects of different stable noises on stochastic resonance systems.
    • Funds: Project supported by the National Natural Science Foundation of China(Grant No.11072182).
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    Benzi R, Sutera A, Vulpiani A 1981 Phys. A 14 453

    [2]

    Gammaitoni L, Hanggi P, Marchesoni F 1998 Rev. Mod. Phys. 70 223

    [3]

    Kang Y M 2004 Ph. D. Dissertation (Xian: Xi’an Jiaotong University) (in Chinese) [康艳梅 2004 博士学位论文 (西安: 西安交通大学)]

    [4]

    Bartussek R, Hanggi P, Jung P 1994 Phys Rev. E 49 3939

    [5]

    Zhu G Q, Ding K, Zhang Y, Zhao Y 2010 Acta Phys. Sin. 59 3001 (in Chinese) [朱光起, 丁珂, 张宇, 赵远 2010 物理学报 59 3001]

    [6]

    Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 物理学报 59 1494]

    [7]

    Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123

    [8]

    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]

    [9]

    Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 物理学报 59 3627]

    [10]

    Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 物理学报 60 060514]

    [11]

    Anishchenko V S, Safonova M A, Chua L O 1993 Journal of Circuit, System and Computer 3 553

    [12]

    Anishchenko V S, Safonova M A, Chua L O 1992 International Journal of Bifurcation and Chaos 2(2) 397

    [13]

    Bulsara A R, Gammaitoni L 1996 Physics Today 3 39

    [14]

    Duan F, Xu B H 2003 Int. J. Bifurcation and Chaos 13 411

    [15]

    Xu B H, Duan F B 2004 Phys. Rev. E 69 061110

    [16]

    Xu B H, Zeng L Z, Li J L 2007 Sound and Vibration 303 255

    [17]

    Xu B H, Zhang H Q, Zeng L Z, Li J L, Wu X X, Jiang Z P 2007 Appl. Phys. Lett. 91 91908

    [18]

    Zhao Z K, Hui G H 2010 Advanced Materials Research 121-122 646

    [19]

    Yang Y B, Xu B H 2011 IUTAM Bookseries 29 229

    [20]

    Jiang S Q, Guo F, Zhou YR, Gu T X 2007 Physcia A: Statistical Mechanics and its Applications 375 483

    [21]

    Nolan J P 2009 Stable distributions (Math/Stat Department, American University) Manuscript, in preparation

    [22]

    Zeng L Z, Xu B H, Li J L 2007 Physics Letters A 455

    [23]

    Li Y J, Kang Y M 2010 Commun. Theor. Phys. 54 292

    [24]

    Kang Y M, Jiang Y L 2008 Chin. Phys. Lett. 25 3578

    [25]

    Zhang L, Song A, He J 2009 Phys. A: Math. Theor. 42 475003

    [26]

    Zhang W Y, Wang Z L, Zhang W D 2009 Control Engineering of China. 16(5) 638 (in Chinese) [张文英, 王自力, 张卫东 2009 控制工程 16 (5) 638]

    [27]

    Di PaolaM , Failla G 2005 Probabilist. Eng. Mech. 20 128

    [28]

    Gitterman M 2000 Phys. Rev. E 62 6065

    [29]

    Yang X L 2003 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [杨祥龙 2003 博士学位论文 (杭州: 浙江大学)]

    [30]

    Janicki A, Weron A 1994 Simulation and Chaotic Behavior of α Stable Stochastic Processes (New York: Marcel Dekker)

    [31]

    Nolan J P 2002 Stable Distributions (Boston: Birkhauser)

    [32]

    Dybiec B, Gudowska-Nowak E 2006 Acta Physica Polonica B 37 1479

    [33]

    Weron A, Weron R 1995 Lecture Notes in Physics 457 379

    [34]

    Weron R 1996 Statist. Prob. Lett 28 165

    [35]

    Weron R 1996 Research Report HSC Wroclaw University of Technology 1 1

    [36]

    Gong C, Wang Z L 2008 MATLAB language commonly used algorithm for assembly (Electronic Industry Press) (in Chinese) [龚纯, 王正林 2008 MATLAB语言常用算法程序集(电子工业出版社)]

    [37]

    Dybiec B, Gudowska-Nowak E 2004 Phys. Rev. E 69 016105

    [38]

    Dybiec B, Gudowska-Nowak E 2004 Fluct. Noise Lett. 4 L273

    [39]

    Gudowska-Nowak E, Dybiec B, Flyvbjerg H 2004 Proc SPIE 5467 223

    [40]

    Bulsara A R, Inchiosa M E, Gammaitoni L 1996 Phys. Rev. Lett. 77 2162

    [41]

    Mitaim S, Kosko B 2004 IEEE Trans. Neural Netw. 15 1526

    [42]

    Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社)]

  • [1]

    Benzi R, Sutera A, Vulpiani A 1981 Phys. A 14 453

    [2]

    Gammaitoni L, Hanggi P, Marchesoni F 1998 Rev. Mod. Phys. 70 223

    [3]

    Kang Y M 2004 Ph. D. Dissertation (Xian: Xi’an Jiaotong University) (in Chinese) [康艳梅 2004 博士学位论文 (西安: 西安交通大学)]

    [4]

    Bartussek R, Hanggi P, Jung P 1994 Phys Rev. E 49 3939

    [5]

    Zhu G Q, Ding K, Zhang Y, Zhao Y 2010 Acta Phys. Sin. 59 3001 (in Chinese) [朱光起, 丁珂, 张宇, 赵远 2010 物理学报 59 3001]

    [6]

    Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 物理学报 59 1494]

    [7]

    Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123

    [8]

    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]

    [9]

    Lin M, Meng Y 2010 Acta Phys. Sin. 59 3627 (in Chinese) [林敏, 孟莹 2010 物理学报 59 3627]

    [10]

    Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 物理学报 60 060514]

    [11]

    Anishchenko V S, Safonova M A, Chua L O 1993 Journal of Circuit, System and Computer 3 553

    [12]

    Anishchenko V S, Safonova M A, Chua L O 1992 International Journal of Bifurcation and Chaos 2(2) 397

    [13]

    Bulsara A R, Gammaitoni L 1996 Physics Today 3 39

    [14]

    Duan F, Xu B H 2003 Int. J. Bifurcation and Chaos 13 411

    [15]

    Xu B H, Duan F B 2004 Phys. Rev. E 69 061110

    [16]

    Xu B H, Zeng L Z, Li J L 2007 Sound and Vibration 303 255

    [17]

    Xu B H, Zhang H Q, Zeng L Z, Li J L, Wu X X, Jiang Z P 2007 Appl. Phys. Lett. 91 91908

    [18]

    Zhao Z K, Hui G H 2010 Advanced Materials Research 121-122 646

    [19]

    Yang Y B, Xu B H 2011 IUTAM Bookseries 29 229

    [20]

    Jiang S Q, Guo F, Zhou YR, Gu T X 2007 Physcia A: Statistical Mechanics and its Applications 375 483

    [21]

    Nolan J P 2009 Stable distributions (Math/Stat Department, American University) Manuscript, in preparation

    [22]

    Zeng L Z, Xu B H, Li J L 2007 Physics Letters A 455

    [23]

    Li Y J, Kang Y M 2010 Commun. Theor. Phys. 54 292

    [24]

    Kang Y M, Jiang Y L 2008 Chin. Phys. Lett. 25 3578

    [25]

    Zhang L, Song A, He J 2009 Phys. A: Math. Theor. 42 475003

    [26]

    Zhang W Y, Wang Z L, Zhang W D 2009 Control Engineering of China. 16(5) 638 (in Chinese) [张文英, 王自力, 张卫东 2009 控制工程 16 (5) 638]

    [27]

    Di PaolaM , Failla G 2005 Probabilist. Eng. Mech. 20 128

    [28]

    Gitterman M 2000 Phys. Rev. E 62 6065

    [29]

    Yang X L 2003 Ph. D. Dissertation (Hangzhou: Zhejiang University) (in Chinese) [杨祥龙 2003 博士学位论文 (杭州: 浙江大学)]

    [30]

    Janicki A, Weron A 1994 Simulation and Chaotic Behavior of α Stable Stochastic Processes (New York: Marcel Dekker)

    [31]

    Nolan J P 2002 Stable Distributions (Boston: Birkhauser)

    [32]

    Dybiec B, Gudowska-Nowak E 2006 Acta Physica Polonica B 37 1479

    [33]

    Weron A, Weron R 1995 Lecture Notes in Physics 457 379

    [34]

    Weron R 1996 Statist. Prob. Lett 28 165

    [35]

    Weron R 1996 Research Report HSC Wroclaw University of Technology 1 1

    [36]

    Gong C, Wang Z L 2008 MATLAB language commonly used algorithm for assembly (Electronic Industry Press) (in Chinese) [龚纯, 王正林 2008 MATLAB语言常用算法程序集(电子工业出版社)]

    [37]

    Dybiec B, Gudowska-Nowak E 2004 Phys. Rev. E 69 016105

    [38]

    Dybiec B, Gudowska-Nowak E 2004 Fluct. Noise Lett. 4 L273

    [39]

    Gudowska-Nowak E, Dybiec B, Flyvbjerg H 2004 Proc SPIE 5467 223

    [40]

    Bulsara A R, Inchiosa M E, Gammaitoni L 1996 Phys. Rev. Lett. 77 2162

    [41]

    Mitaim S, Kosko B 2004 IEEE Trans. Neural Netw. 15 1526

    [42]

    Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社)]

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  • Received Date:  03 May 2011
  • Accepted Date:  15 June 2011
  • Published Online:  15 April 2012

Parameter-induced stochastic resonance in overdamped system with stable noise

  • 1. Department of Applied Mathematics, School of Science, Xi’an Jiaotong University, Xi’an 710049, China
Fund Project:  Project supported by the National Natural Science Foundation of China(Grant No.11072182).

Abstract: Parameter-induced stochastic resonance is an important method of detecting weak signal from noise, but under stable noise background, this method has not been reported. In this paper, we study the parameter-induced stochastic resonance in an overdamped system with stable noise. Our investigation discloses that the stochastic resonance can be realized by tuning the system parameter under stable noise background; when the nonlinear term parameter is turned, the resonant effect becomes weakened as the stability index decreases. But when the linear term parameter is turned, the resonant effect becomes strengthened as the stability index decreases. Our observation is significant for understanding the positive role of stable noise in weak signal detection, which is helpful for understanding the effects of different stable noises on stochastic resonance systems.

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