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In this paper we take the asymmetric bistable system excited by weak periodic signal as a model and regard signal-to-noise ratio gain as an index to investigate the stochastic resonance phenomenon stimulated by additive and multiplicative α stable noise. Stochastic resonance phenomenon stimulated by only additive α stable noise is also investigated here. The laws for the resonance system parameters a, b, asymmetric skewness r and intensity amplification factor Q or D of α stable noise to act on the resonant output are explored under different stability index α and skewness parameter β of α stable noise. The results show that no matter whether under the joint action of additive and multiplicative α stable noise or under the action of only additive α stable noise, weak signal detection can be realized by tuning the system parameters a, b and r. The intervals of a, b and r which can induce stochastic resonances are multiple, and do not change with α nor β. Moreover, when investigating the noise-induced stochastic resonance, it is found that stochastic resonance can also be realized by tuning the intensity amplification factor of α stable noise. And the interval of D does not change with α nor β. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.
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Keywords:
- α stable noise /
- asymmetric bistable system /
- stochastic resonance /
- signal-to-noise ratio gain
[1] 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]
[2] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin. 52 2405 (in Chinese) [祝恒江, 李蓉, 温孝东 2003 52 2405]
[3] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广 2005 54 1118]
[4] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 396 (in Chinese) [肖方红, 闫桂荣, 韩雨航 2004 53 396]
[5] Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[6] Li J L, Xu B H 2006 Chin. Phys. B 15 2867
[7] Li J L 2009 Chin. Phys. B 18 5196
[8] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 58 5196]
[9] 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]
[10] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[11] Li J H 2002 Phys. Rev. E 66 031104
[12] Zhou B C, Xu W 2008 Acta Phys. Sin. 57 2035 (in Chinese) [周丙常, 徐伟 2008 57 2035]
[13] 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]
[14] 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]
[15] Jiao S B, Ren C, Li P H, Zhang Q, Xie G 2013 Acta Phys. Sin. 63 070501 (in Chinese) [焦尚彬, 任超, 李鹏华, 张青, 谢国 2013 63 070501]
[16] Leng Y G, Wang T Y, Guo Y, Wu Z Y 2007 Acta Phys. Sin. 56 30 (in Chinese) [冷永刚, 王太勇, 郭焱, 吴振勇 2007 56 30]
[17] 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]
[18] Jin Y F, Xu W, Xu M 2005 Chaos, Soliton. Fract. 26 1183
[19] Leccardi M 2005 ENOC'O5 (Fifth EUROMECH Nonlinear Dynamics Conference) Eindhoven, The Netherland 2005
[20] Nolan J P 1999 Math. Comput. Model 29 229
[21] Tang Y, Zou W, Lu J Q, Kurths J 2012 Phys. Rev. E 85 046207
[22] Dybiec B, Gudowska-Nowak E 2006 Acta Phys. Pol. B 37 1479
[23] Liang Y J, Chen W 2013 Signal Process. 93 242
[24] Jiao S B, He T 2013 Comput. Engineer. Appl. 50 221 (in Chinese) [焦尚彬, 何童 2013 计算机工程与应用 50 221]
[25] Xu W, Jin Y F, Xu M, Li W 2005 Acta Phys. Sin. 54 2405 (in Chinese) [徐伟, 靳艳飞, 徐猛, 李伟 2005 54 2405]
[26] Gong D C, Qin G R, Hu G, Wen X D 1992 Sci. China A 8 828 (in Chinese) [龚德纯, 秦光戎, 胡岗, 温孝东 1992 中国科学A辑 8 828]
[27] 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]
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[1] 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]
[2] Zhu H J, Li R, Wen X D 2003 Acta Phys. Sin. 52 2405 (in Chinese) [祝恒江, 李蓉, 温孝东 2003 52 2405]
[3] Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广 2005 54 1118]
[4] Xiao F H, Yan G R, Han Y H 2004 Acta Phys. Sin. 53 396 (in Chinese) [肖方红, 闫桂荣, 韩雨航 2004 53 396]
[5] Jiang S Q, Hou M J, Jia C H, He J R, Gu T X 2009 Chin. Phys. B 18 2667
[6] Li J L, Xu B H 2006 Chin. Phys. B 15 2867
[7] Li J L 2009 Chin. Phys. B 18 5196
[8] Leng Y G 2009 Acta Phys. Sin. 58 5196 (in Chinese) [冷永刚 2009 58 5196]
[9] 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]
[10] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
[11] Li J H 2002 Phys. Rev. E 66 031104
[12] Zhou B C, Xu W 2008 Acta Phys. Sin. 57 2035 (in Chinese) [周丙常, 徐伟 2008 57 2035]
[13] 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]
[14] 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]
[15] Jiao S B, Ren C, Li P H, Zhang Q, Xie G 2013 Acta Phys. Sin. 63 070501 (in Chinese) [焦尚彬, 任超, 李鹏华, 张青, 谢国 2013 63 070501]
[16] Leng Y G, Wang T Y, Guo Y, Wu Z Y 2007 Acta Phys. Sin. 56 30 (in Chinese) [冷永刚, 王太勇, 郭焱, 吴振勇 2007 56 30]
[17] 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]
[18] Jin Y F, Xu W, Xu M 2005 Chaos, Soliton. Fract. 26 1183
[19] Leccardi M 2005 ENOC'O5 (Fifth EUROMECH Nonlinear Dynamics Conference) Eindhoven, The Netherland 2005
[20] Nolan J P 1999 Math. Comput. Model 29 229
[21] Tang Y, Zou W, Lu J Q, Kurths J 2012 Phys. Rev. E 85 046207
[22] Dybiec B, Gudowska-Nowak E 2006 Acta Phys. Pol. B 37 1479
[23] Liang Y J, Chen W 2013 Signal Process. 93 242
[24] Jiao S B, He T 2013 Comput. Engineer. Appl. 50 221 (in Chinese) [焦尚彬, 何童 2013 计算机工程与应用 50 221]
[25] Xu W, Jin Y F, Xu M, Li W 2005 Acta Phys. Sin. 54 2405 (in Chinese) [徐伟, 靳艳飞, 徐猛, 李伟 2005 54 2405]
[26] Gong D C, Qin G R, Hu G, Wen X D 1992 Sci. China A 8 828 (in Chinese) [龚德纯, 秦光戎, 胡岗, 温孝东 1992 中国科学A辑 8 828]
[27] 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]
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