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研究了高斯色噪声和周期信号共同作用下非对称双稳耦合网络系统的协同效应. 此系统是由大量振荡器组成的网络模型, 个体与个体之间的相互运作、变化产生出复杂的非线性行为模式. 为了进行深入研究, 首先, 运用平均场理论、统一色噪声近似理论和等效非线性化等方法对原始
$ N $ 维系统进行降维近似. 其次, 借助役使原理得到简化模型的郎之万方程, 进一步根据两态模型理论推导出信噪比的理论表达式, 基于此发现系统产生了尺度随机共振现象. 最后, 分析了高斯色噪声、系统参数和周期信号等对非对称耦合网络系统随机共振行为的影响. 结果表明, 高斯色噪声自关联时间和噪声强度的增大, 能够促进尺度随机共振现象; 选取合适的耦合系数能使系统随机共振效应达到最佳. 此外, 还比较了高斯色噪声和高斯白噪声分别驱动下系统的随机共振问题, 发现高斯色噪声更有利于增强随机共振现象.-
关键词:
- 随机共振 /
- 非对称双稳耦合网络系统 /
- 信噪比 /
- 高斯色噪声
In this work studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal. The system is a network model consisting of a large number of oscillators. The interaction and change between individuals produce complex nonlinear behavior patterns. For further research, firstly, the original N-dimensional system is reduced and approximated by using the mean field theory, the unified colored noise approximation theory and the equivalent nonlinearization method. Secondly, the Langevin equation of simplified model is obtained through the slaving principle by using the two-state model theory to derive the theoretical expression of signal-to-noise ratio. It is found that the system produces the phenomenon of scale stochastic resonance. Finally, the effects of Gaussian color noise parameters, system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed. The results show that the increase of Gaussian colored noise correlation time and noise intensity can promote the scale stochastic resonance phenomenon; selecting appropriate coupling coefficient can achieve the optimal stochastic resonance effect. And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise, respectively, are analyzed and compared with each other. Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.-
Keywords:
- stochastic resonance /
- asymmetric bistable coupled network systems /
- signal-to-noise ratio /
- Gaussian colored noise
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Wu X H 2010 M. S. Thesis (Nanjing: Nanjing University of Aeronautics and Astronautics) (in Chinese)
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图 2 SNR作为系统尺度N的函数关于不同自关联时间
$ \tau $ 的关系图Fig. 2. Relationship of SNR as a function of system scale N with different correlation time
$ \tau $ .
图 3 噪声强度D对输出信噪比SNR的影响 (a) SNR作为系统尺度N的函数关于D变化的曲线; (b) 分别由高斯色噪声、高斯白噪声驱动下系统输出SNR的对比
Fig. 3. The influence of noise intensity D on the output SNR: (a) Curve of SNR as a function of the system scale N with the change of D; (b) comparison of system output SNR driven by Gaussian colored noises and Gaussian white noises respectively.
图 4 耦合系数
$ {\theta } $ 对输出信噪比SNR的影响 (a) SNR作为系统尺度N的函数关于$ \theta $ 的变化曲线; (b) 分别由高斯色噪声、高斯白噪声驱动下系统输出SNR的对比Fig. 4. The influence of coupling coefficient
$ \theta $ on the output SNR: (a) Curve of SNR as a function of the system scale N with the change of$ \theta $ ; (b) comparison of system output SNR driven by Gaussian colored noises and Gaussian white noises respectively.
图 6 SNR作为噪声强度D的函数关于不同系统尺度N的关系图
Fig. 6. Relationship of SNR as a function of noise intensity D with different system scale N.
图 5 SNR作为系统尺度N的函数关于不同非对称性系数r的关系图
Fig. 5. Relationship of SNR as a function of system scale N with different asymmetric coefficient r.
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[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
Google Scholar
[2] Mc Namara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
Google Scholar
[3] Dykman M I, Luchinsky D G, Mannella R, McClintock P V E, Stein N D, Stocks N G 1993 J. Stat. Phys. 70 463
Google Scholar
[4] Zhou T, Moss F, Jung P 1990 Phys. Rev. A 42 3161
Google Scholar
[5] 武娟 2018 博士学位论文 (西安: 西北工业大学)
Wu J 2018 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University) (in Chinese)
[6] 曲良辉, 都琳, 曹子露, 胡海威, 邓子辰 2020 物理学报 69 230501
Google Scholar
Qu L H, Du L, Cao Z L, Hu H W, Deng Z C 2020 Acta Phys. Sin. 69 230501
Google Scholar
[7] 乔岩茹, 陈健龙, 侯文 2021 电子测量技术 44 88
Google Scholar
Qiao Y R, Chen J L, Hou W 2021 Electron. Meas. Technol. 44 88
Google Scholar
[8] 靳艳飞, 李贝 2014 物理学报 63 210501
Google Scholar
Jin Y F, Li B 2014 Acta Phys. Sin. 63 210501
Google Scholar
[9] 张晓燕, 徐伟, 周丙常 2011 物理学报 60 060514
Google Scholar
Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514
Google Scholar
[10] Hänggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
Google Scholar
[11] 焦尚彬, 李佳, 张青, 谢国 2016 系统仿真学报 28 139
Google Scholar
Jiao S B, Li J, Zhang Q, Xie G 2016 J. Syst. Phys. Simul. 28 139
Google Scholar
[12] Zhang X Y, Zheng X Y 2019 Indian J. Phys. 93 1051
Google Scholar
[13] 杨建华, 马强, 吴呈锦, 刘后广 2018 物理学报 67 054501
Google Scholar
Yang J H, Ma Q, Wu C J, Liu H G 2018 Acta Phys. Sin. 67 054501
Google Scholar
[14] 俞莹丹, 林敏, 黄咏梅, 徐明 2021 物理学报 70 040501
Google Scholar
Yu Y D, Lin M, Huang Y M, Xu M 2021 Acta Phys. Sin. 70 040501
Google Scholar
[15] 马圣楠 2019 硕士学位论文 (北京: 华北电力大学)
Ma S N 2019 M. S. Thesis (Beijing: North China Electric Power University) (in Chinese)
[16] 何传磊 2020 硕士学位论文 (成都: 西南交通大学)
He C L 2020 M. S. Thesis (Chengdu: Southwest Jiaotong University) (in Chinese)
[17] 刘小强 2019 硕士学位论文 (西安: 陕西师范大学)
Liu X Q 2019 M. S. Thesis (Xi’an: Shanxi Normal University) (in Chinese)
[18] 孙中奎, 鲁捧菊, 徐伟 2014 物理学报 63 92
Google Scholar
Sun Z K, Lu P J, Xu W 2014 Acta Phys. Sin. 63 92
Google Scholar
[19] Kometani K, Shimizu H 1975 J. Stat. Phys. 13 473
Google Scholar
[20] Pikovsky A S, Rateitschak K, Kurth S 1994 Z. Phys. B 95 541
[21] 朱位秋 2017 随机动力学引论 (北京: 科学出版社) 第 73—75 页
Zhu W Q 2017 Introduction to Stochastic Dynamics (Beijing: Science Press) pp73–75 (in Chinese)
[22] 严惠云, 师义民, 苏剑, 李爽 2016 西安交通大学学报 50 141
Google Scholar
Yan H Y, Shi Y M, Su J, Li S 2016 J. Xi’an. Jiaotong Univ. 50 141
Google Scholar
[23] Li C, Da-Jin W, Sheng-Zhi K 1995 Phys. Rev. E 52 3228
[24] Cubero D 2008 Phys. Rev. E 77 021112
Google Scholar
[25] 吴大进, 曹力, 陈立华 1990 协同学原理和应用 (武汉: 华中理工大学出版社) 第 67—93 页
Wu D J, Cao L, Chen L H 1990 Principles and Applications in Synergistics (Wuhan: Huazhong University of Science and Technology Press) pp67–93 (in Chinese)
[26] Novikov E A 1965 Sov. Phys. JETP 20 1290
[27] 宁丽娟, 徐伟, 杨晓丽 2007 物理学报 56 25
Google Scholar
Ning L J, Xu W, Yang X L 2007 Acta Phys. Sin. 56 25
Google Scholar
[28] 胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社) 第 131—135 页
Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technoogical Education Publishing House) pp131–135 (in Chinese)
[29] Mc Namara B, Wiesenfeld K 1989 Physical Review A 39 4854
[30] 吴志会 2010 硕士学位论文 (南京: 南京航空航天大学)
Wu X H 2010 M. S. Thesis (Nanjing: Nanjing University of Aeronautics and Astronautics) (in Chinese)
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