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以微弱周期信号激励的非对称双稳系统为模型, 以信噪比增益为指标, 首先针对加性和乘性α 稳定噪声共同作用的随机共振现象展开了研究, 然后针对单独加性α 稳定噪声激励的随机共振现象进行了研究, 探究了α 稳定噪声特征指数α 和对称参数β 分别取不同值时, 系统结构参数a, b, 刻画双稳系统非对称性的偏度r以及α 稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律. 研究结果表明, 无论在加性和乘性α 稳定噪声共同作用下还是在单独加性α 稳定噪声作用下, 通过调节a和b或者r均可诱导随机共振, 实现微弱信号的检测, 且有多个参数区间与之对应, 这些区间不随α 或β 的变化而变化; 在研究噪声诱导的随机共振现象时发现, 调节噪声强度放大系数也可使系统产生随机共振现象, 且达到共振状态时D的区间也不随α 或β 的变化而变化. 这些结论为α 稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.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
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[10] Zhang J J, Jin Y F 2011 Acta Phys. Sin. 60 120501 (in Chinese) [张静静, 靳艳飞 2011 60 120501]
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[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]
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[19] Leccardi M 2005 ENOC'O5 (Fifth EUROMECH Nonlinear Dynamics Conference) Eindhoven, The Netherland 2005
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[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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