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A periodic potential system excited by multi-low frequency weak signals, the high frequency signal and additive stable noise is constructed. Based on this model, the vibrational resonance phenomenon under stable noise is investigated by taking the mean signal-noise-ratio gain (MSNRI) of output as a performance index. Then the influences of stability index (0 2), the skewness parameter (-1 1) of stable noise, the amplification factor D and the high frequency signal amplitude B, and frequency on the resonant output effect are explored. The results show that under the different distributions of stable noise, the multi-low frequency weak signals detection can be realized by adjusting the high frequency signal parameter B or to induce vibrational resonance within a certain range. When (or ) is given different values, the curve of MSNRI-B has multiple peaks with the increase of B for a certain frequency , and the values of MSNRI corresponding to peaks of the curve of MSNRI-B are equal. So the intervals of B which can induce vibrational resonances are multiple, and the multiple resonance phenomenon turns periodic with the increase of B. Similarly, the curve of MSNRI- also has multiple peaks with the increase of for a certain amplitude B, so the intervals of which can induce vibrational resonances are also multiple. The difference is that the multiple resonance phenomenon becomes irregular with the increase of . Besides, the resonance intervals of B and do not change with nor . Under the different values of amplitude factor D, the resonance intervals of B (or ) do not change with the increase of D, indicating that only the energy of the high frequency signal transfers toward the signals to be measured, and the energy of stable noise does not transfer toward the signals to be measured. Besides, when B and are fixed, it can still be realized to detect the weak signal with the increase of D, which shows that the weak signal detection method based on vibrational resonance can overcome the shortcoming that noise intensity in industrial sites cannot be regulated and controlled. The results provide a new method of detecting the weak signal, and have potential application value in signal processing.
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Keywords:
- vibrational resonance /
- a periodic potential system /
- multi-low frequency weak signals detection /
- the mean of signal-noise-ratio gain
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[2] Chizhevsky V N, Smeu E, Giacomelli G 2008 U. P. B. Bull. Ser. A 70 31
[3] Yang J H 2011 Ph. D. Dissertation (Nanjing: University of Aeronautics and Astronautics) (in Chinese) [杨建华 2010 博士学位论文 (南京: 航天航空大学)]
[4] Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433
[5] Gitterman M 2001 J. Phys. A: Math. Gen. 34 L355
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[7] Chizhevsky V N 2007 Int. J. Bifurcat. Chaos 18 1767
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[9] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6713 (in Chinese) [林敏, 黄咏梅 2007 物理学报 56 6713]
[10] Yang J H, Liu X B 2010 J. Phys. A 43 122001
[11] Yang J H, Liu X B 2012 Acta Phys. Sin. 61 010505 (in Chinese) [杨建华, 刘先斌 2012 物理学报 61 010505]
[12] Yang X N, Yang Y F 2015 Acta Phys. Sin. 64 070507 (in Chinese) [杨秀妮, 杨云峰 2015 物理学报 64 070507]
[13] Blekhman I I, Landa P S 2004 Non-Linear Mech. 39 421
[14] Ullner E, Zaikin A, García-Ojalvo J 2003 Phys. Lett. A 312 348
[15] Deng B, Wang J, Wei X 2009 Chaos 19 013117
[16] Yu H T, Guo X M, Wang J, Deng B, Wei X L 2015 J. Phys. A 436 170
[17] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A 2009 Chaos 19 043128
[18] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A 2009 Phys. Rev. E 80 046608
[19] Yang J H, Liu H G, Cheng G 2013 Acta Phys. Sin. 62 180503
[20] Mbong T L M D, Siewe M S, Tchawoua C 2016 Mech. Res. Commun. 78 13
[21] Chizhevsky V N, Smeu E, Giacomelli G 2003 Phys. Rev. Lett. 91 220602
[22] Chizhevsky V N 2014 Phys. Rev. E 90 042924
[23] Zaikin A A, Lopez L, Baltanas J P, Kurths J, Sanjuan M A F 2002 Phys. Rev. E 66 011106
[24] Casado-Pascual J, Baltanas J P 2004 Phys. Rev. E 69 059902
[25] Chizhevsky V N, Giacomelli G 2008 Phys. Rev. E 77 051126
[26] Yang J H, Liu X B 2010 Chaos 20 033124
[27] 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]
[28] 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]
[29] Liang Y J, Chen W 2013 Signal Process. 93 242
[30] 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]
[31] Zeng L Z, Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175
[32] Fogedby H C 1998 Phys. Rev. E 58 1690
[33] Zeng L Z, Xu B H 2010 J. Phys. A: Statist. Mech. Appl. 389 5128
[34] 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]
[35] Weron R 1996 Statist. Prob. Lett. 28 165
[36] Wan P, Zhan Y J, Li X C 2011 Acta Phys. Sin. 60 040502 (in Chinese) [万频, 詹宜巨, 李学聪 2011 物理学报 60 040502]
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[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 453
[2] Chizhevsky V N, Smeu E, Giacomelli G 2008 U. P. B. Bull. Ser. A 70 31
[3] Yang J H 2011 Ph. D. Dissertation (Nanjing: University of Aeronautics and Astronautics) (in Chinese) [杨建华 2010 博士学位论文 (南京: 航天航空大学)]
[4] Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433
[5] Gitterman M 2001 J. Phys. A: Math. Gen. 34 L355
[6] Baltanás J P, López L, Blechman I I, Landa P S 2003 Phys. Rev. E 67 066119
[7] Chizhevsky V N 2007 Int. J. Bifurcat. Chaos 18 1767
[8] Lin M, Huang Y M 2007 Vib. Shock 12 151 (in Chinese) [林敏, 黄咏梅 2007 振动与冲击 12 151]
[9] Lin M, Huang Y M 2007 Acta Phys. Sin. 56 6713 (in Chinese) [林敏, 黄咏梅 2007 物理学报 56 6713]
[10] Yang J H, Liu X B 2010 J. Phys. A 43 122001
[11] Yang J H, Liu X B 2012 Acta Phys. Sin. 61 010505 (in Chinese) [杨建华, 刘先斌 2012 物理学报 61 010505]
[12] Yang X N, Yang Y F 2015 Acta Phys. Sin. 64 070507 (in Chinese) [杨秀妮, 杨云峰 2015 物理学报 64 070507]
[13] Blekhman I I, Landa P S 2004 Non-Linear Mech. 39 421
[14] Ullner E, Zaikin A, García-Ojalvo J 2003 Phys. Lett. A 312 348
[15] Deng B, Wang J, Wei X 2009 Chaos 19 013117
[16] Yu H T, Guo X M, Wang J, Deng B, Wei X L 2015 J. Phys. A 436 170
[17] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A 2009 Chaos 19 043128
[18] Jeyakumari S, Chinnathambi V, Rajasekar S, Sanjuan M A 2009 Phys. Rev. E 80 046608
[19] Yang J H, Liu H G, Cheng G 2013 Acta Phys. Sin. 62 180503
[20] Mbong T L M D, Siewe M S, Tchawoua C 2016 Mech. Res. Commun. 78 13
[21] Chizhevsky V N, Smeu E, Giacomelli G 2003 Phys. Rev. Lett. 91 220602
[22] Chizhevsky V N 2014 Phys. Rev. E 90 042924
[23] Zaikin A A, Lopez L, Baltanas J P, Kurths J, Sanjuan M A F 2002 Phys. Rev. E 66 011106
[24] Casado-Pascual J, Baltanas J P 2004 Phys. Rev. E 69 059902
[25] Chizhevsky V N, Giacomelli G 2008 Phys. Rev. E 77 051126
[26] Yang J H, Liu X B 2010 Chaos 20 033124
[27] 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]
[28] 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]
[29] Liang Y J, Chen W 2013 Signal Process. 93 242
[30] 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]
[31] Zeng L Z, Bao R H, Xu B H 2007 J. Phys. A: Math. Theor. 40 7175
[32] Fogedby H C 1998 Phys. Rev. E 58 1690
[33] Zeng L Z, Xu B H 2010 J. Phys. A: Statist. Mech. Appl. 389 5128
[34] 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]
[35] Weron R 1996 Statist. Prob. Lett. 28 165
[36] Wan P, Zhan Y J, Li X C 2011 Acta Phys. Sin. 60 040502 (in Chinese) [万频, 詹宜巨, 李学聪 2011 物理学报 60 040502]
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