An underdamped and delayed tri-stable model-based stochastic resonance

doi:10.1088/1674-1056/ad01a6

中国物理B ›› 2024, Vol. 33 ›› Issue (1): 10501-10501.doi: 10.1088/1674-1056/ad01a6

An underdamped and delayed tri-stable model-based stochastic resonance

Yan-Fei Jin(靳艳飞)^†, Hao-Tian Wang(王昊天), and Ting-Ting Zhang(张婷婷)

Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2023-09-11 修回日期:2023-10-07 接受日期:2023-10-10 出版日期:2023-12-13 发布日期:2024-01-03
通讯作者: Yan-Fei Jin E-mail:jinyf@bit.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12072025) and the Beijing Natural Science Foundation (Grant No. 1222015).

An underdamped and delayed tri-stable model-based stochastic resonance

Yan-Fei Jin(靳艳飞)^†, Hao-Tian Wang(王昊天), and Ting-Ting Zhang(张婷婷)

Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China

Received:2023-09-11 Revised:2023-10-07 Accepted:2023-10-10 Online:2023-12-13 Published:2024-01-03
Contact: Yan-Fei Jin E-mail:jinyf@bit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12072025) and the Beijing Natural Science Foundation (Grant No. 1222015).

摘要/Abstract

摘要： Stochastic resonance (SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density (SPD) and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations (MCS) confirm the effectiveness of the theoretical results.

关键词: stochastic resonance, underdamped tri-stable system, spectral amplification, time-delayed feedback

Abstract: Stochastic resonance (SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density (SPD) and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations (MCS) confirm the effectiveness of the theoretical results.

Key words: stochastic resonance, underdamped tri-stable system, spectral amplification, time-delayed feedback

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

02.50.-r (Probability theory, stochastic processes, and statistics)

Yan-Fei Jin(靳艳飞), Hao-Tian Wang(王昊天), and Ting-Ting Zhang(张婷婷). An underdamped and delayed tri-stable model-based stochastic resonance[J]. 中国物理B, 2024, 33(1): 10501-10501.

Yan-Fei Jin(靳艳飞), Hao-Tian Wang(王昊天), and Ting-Ting Zhang(张婷婷). An underdamped and delayed tri-stable model-based stochastic resonance[J]. Chin. Phys. B, 2024, 33(1): 10501-10501.

参考文献

[1] Gammaitoni L, Hanggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] Hu G, Ditzinger T, Ning C Z and Haken H 1993 Phys. Rev. Lett. 71 807
[3] Douglass J K, Wilkens L, Pantazelou E and Moss F 1993 Nature 365 337
[4] Zhou T and Moss F 1990 Phys. Rev. A 41 4255
[5] Kenfack A and Singh K P 2010 Phys. Rev. E 82 046224
[6] Yang T T, Zhang H Q, Xu Y and Xu W 2014 Int. J. Nonlinear Mech. 67 42
[7] Laas K, Mankin R and Rekker A 2009 Phys. Rev. E 79 051128
[8] Jin Y F 2018 Chin. Phys. B 27 050501
[9] Jin Y F, Ma Z M and Xiao S M 2017 Chaos, Solitons & Fractals 103 470
[10] Liu R N and Kang Y M 2018 Phys. Lett. A 382 1656
[11] Ding Y M, Kang Y M and Zhai Y J 2023 IEEE Transactions on Instrumentation and Measurement 72 3510812
[12] Zhang T T, Jin Y F and Zhang Y X 2023 J. Sound Vib. 543 117379
[13] Zhou S X, Cao J Y, Inman D J, Lin J and Li D 2016 J. Sound Vib. 373 223
[14] Zhou B L, Jin Y F and Xu H D 2022 Appl. Math. Model. 108 427
[15] Melancon D, Gorissen B, Garcia-Mora C J, Hoberman C and Bertoldi K 2021 Nature 592 545
[16] Jin Y F and Wang H Q 2020 Chaos, Solitons & Fractals 133 109633
[17] Masoller C 2002 Phys. Rev. Lett. 88 034102
[18] Martínez-Zérega B E and Pisarchik A N 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 4023
[19] Kraut S and Feudel U 2002 Phys. Rev. E 66 015207
[20] Nicolis C 2010 Phys. Rev. E 82 011139
[21] Nicolis G and Nicolis C 2016 Entropy 18 172
[22] Xu P F and Jin Y F 2020 Chaos, Solitons & Fractals 138 109857
[23] Jin Y F and Wang H Q 2021 Chin. J. Theor. Appl. Mech. 53 865
[24] Zhang H Q, Xu Y, Xu W and Li X C 2012 Chaos 22 043130
[25] Arathi S and Rajasekar S 2011 Phys. Scr. 84 065011
[26] Jin Y F, Wang H T, Xu P F and Xie W X 2023 Probabilist. Eng. Mech. 72 103418
[27] Pyragas K 1992 Phys. Lett. A 170 421
[28] Just W, Bernard T, Ostheimer M, Reibold E and Benner H 1997 Phys. Rev. Lett. 78 203
[29] Hu H Y and Wang Z H 1998 J. Sound Vibr 214 213
[30] Guillouzic S, L'Heureux I and Longtin A 1999 Phys. Rev. E 59 3970
[31] Elbeyli O, Sun J Q and Unal G 2005 Commun. Nonlinear Sci. 10 85
[32] Tsimring L S and Pikovsky A 2001 Phys. Rev. Lett. 87 250602
[33] Jin Y F 2012 Physica A 391 1928
[34] Jin Y F, Wang H T and Xu P F 2023 Chaos, Solitons & Fractals 168 113099
[35] Xu P F, Jin Y F and Xiao S M 2017 Chaos 27 113109
[36] Li W J, Ren L H and Duan F B 2022 Chin. Phys. B 31 080503

An underdamped and delayed tri-stable model-based stochastic resonance

An underdamped and delayed tri-stable model-based stochastic resonance

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yuqing Zhang(张宇青) and Youming Lei(雷佑铭). Logical stochastic resonance in a cross-bifurcation non-smooth system[J]. 中国物理B, 2024, 33(3): 38201-038201.
[2]	Rui Gao(高蕊), Shangbin Jiao(焦尚彬), and Qiongjie Xue(薛琼婕). Research and application of composite stochastic resonance in enhancement detection[J]. 中国物理B, 2024, 33(1): 10203-10203.
[3]	Jiangling Liu(刘江令), Chaorun Li(李朝润), Hailing Gao(高海玲), and Luchun Du(杜鲁春). Vibrational resonance in globally coupled bistable systems under the noise background[J]. 中国物理B, 2023, 32(7): 70502-070502.
[4]	Shangbin Jiao(焦尚彬), Rui Gao(高蕊), Qiongjie Xue(薛琼婕), and Jiaqiang Shi(史佳强). Weak signal detection method based on novel composite multistable stochastic resonance[J]. 中国物理B, 2023, 32(5): 50202-050202.
[5]	Yong-Tao Yu(于永涛) and Xiao-Li Yang(杨晓丽). Inverse stochastic resonance in modular neural network with synaptic plasticity[J]. 中国物理B, 2023, 32(3): 30201-030201.
[6]	Huamei Yang(杨华美) and Yuangen Yao(姚元根). Realizing reliable XOR logic operation via logical chaotic resonance in a triple-well potential system[J]. 中国物理B, 2023, 32(2): 20501-020501.
[7]	Haiyou Deng(邓海游), Rong Gui(桂容), and Yuangen Yao(姚元根). Temperature-induced logical resonance in the Hodgkin-Huxley neuron[J]. 中国物理B, 2023, 32(12): 120501-120501.
[8]	Zhi-Kun Li(李智坤) and Dong-Xi Li(李东喜). Inhibitory effect induced by fractional Gaussian noise in neuronal system[J]. 中国物理B, 2023, 32(1): 10203-010203.
[9]	Weijin Li(李伟进), Yuhao Ren(任昱昊), and Fabing Duan(段法兵). Hyperparameter on-line learning of stochastic resonance based threshold networks[J]. 中国物理B, 2022, 31(8): 80503-080503.
[10]	Zhao-Rui Li(李召瑞), Bo-Hang Chen(陈博航), Hui-Xian Sun(孙慧贤), Guang-Kai Liu(刘广凯), and Shi-Lei Zhu(朱世磊). A sign-function receiving scheme for sine signals enhanced by stochastic resonance[J]. 中国物理B, 2021, 30(8): 80502-080502.
[11]	Lei Jiang(姜磊), Li Lai(赖莉), Tao Yu(蔚涛), Maokang Luo(罗懋康). Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency[J]. 中国物理B, 2021, 30(6): 60502-060502.
[12]	Yuangen Yao(姚元根). Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system[J]. 中国物理B, 2021, 30(6): 60503-060503.
[13]	石婷婷, 许雪梅, 孙克辉, 丁一鹏, 黄国伟. Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback[J]. 中国物理B, 2020, 29(5): 50501-050501.
[14]	周永辉, 许雪梅, 尹林子, 丁一鹏, 丁家峰, 孙克辉. Novel Woods-Saxon stochastic resonance system for weak signal detection[J]. 中国物理B, 2020, 29(4): 40503-040503.
[15]	靳艳飞. Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal[J]. 中国物理B, 2018, 27(5): 50501-050501.