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

doi:10.1088/1674-1056/ad01a6

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.

Keywords: stochastic resonance underdamped tri-stable system spectral amplification time-delayed feedback

Received: 11 September 2023
Revised: 07 October 2023
Accepted manuscript online: 10 October 2023

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	02.50.-r	(Probability theory, stochastic processes, and statistics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12072025) and the Beijing Natural Science Foundation (Grant No. 1222015).

Corresponding Authors: Yan-Fei Jin
E-mail: jinyf@bit.edu.cn

Cite this article:

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 2024 Chin. Phys. B 33 010501

[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

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

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention