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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.
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Keywords:
- monostable stochastic resonance /
- α stable noise /
- weak signal detection /
- mean of signal-to-noise ratio gain
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[4] Zhang W, Xiang B R 2006 Talanta 70 267
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[8] Zhou Y R 2011 Chin. Phys. B 20 010501
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[19] Zeng L Z, Xu B H 2010 Journal of physics A: Statistical Mechanics and its Applications 22 5128
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[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 61 040501]
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[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 62 210501]
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[26] Liang Y J, Chen W 2013 Signal Processing 93 242
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[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 60 040502]
[30] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese)[冷永刚, 王太勇2003 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 53 0717]
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[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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[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 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 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 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 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 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 60 040502]
[30] Leng Y G, Wang T Y 2003 Acta Phys. Sin. 52 2432 (in Chinese)[冷永刚, 王太勇2003 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 53 0717]
[32] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese)[冷永刚2009 58 5196]
[33] Lin M, Huang Y M 2006 Acta Phys. Sin. 55 3277 (in Chinese)[林敏, 黄咏梅2006 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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