Logical stochastic resonance in a cross-bifurcation non-smooth system

doi:10.1088/1674-1056/acf11e

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 38201-038201.doi: 10.1088/1674-1056/acf11e

Logical stochastic resonance in a cross-bifurcation non-smooth system

Yuqing Zhang(张宇青)¹ and Youming Lei(雷佑铭)^1,2,†

1 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2023-06-09 修回日期:2023-08-08 接受日期:2023-08-17 出版日期:2024-02-22 发布日期:2024-02-22
通讯作者: Youming Lei E-mail:leiyouming@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12072262) and the Shaanxi Computer Society & Xiangteng Company Foundation.

Logical stochastic resonance in a cross-bifurcation non-smooth system

Yuqing Zhang(张宇青)¹ and Youming Lei(雷佑铭)^1,2,†

1 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China;
2 Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China

Received:2023-06-09 Revised:2023-08-08 Accepted:2023-08-17 Online:2024-02-22 Published:2024-02-22
Contact: Youming Lei E-mail:leiyouming@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12072262) and the Shaanxi Computer Society & Xiangteng Company Foundation.

摘要/Abstract

摘要： This paper investigates logical stochastic resonance (LSR) in a cross-bifurcation non-smooth system driven by Gaussian colored noise. In this system, a bifurcation parameter triggers a transition between monostability, bistability and tristability. By using Novikov's theorem and the unified colored noise approximation method, the approximate Fokker-Planck equation is obtained. Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations. We simulate the logic operation of the system in the bistable and tristable regions respectively. We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter. Furthermore, it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region, since the tristable region is more sensitive to noise than the bistable one.

关键词: logical stochastic resonance, bifurcation, mean first passage time

Abstract: This paper investigates logical stochastic resonance (LSR) in a cross-bifurcation non-smooth system driven by Gaussian colored noise. In this system, a bifurcation parameter triggers a transition between monostability, bistability and tristability. By using Novikov's theorem and the unified colored noise approximation method, the approximate Fokker-Planck equation is obtained. Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations. We simulate the logic operation of the system in the bistable and tristable regions respectively. We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter. Furthermore, it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region, since the tristable region is more sensitive to noise than the bistable one.

Key words: logical stochastic resonance, bifurcation, mean first passage time

中图分类号: (Oscillations, chaos, and bifurcations)

82.40.Bj

05.10.Gg (Stochastic analysis methods) 87.10.Rt (Monte Carlo simulations)

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.

Yuqing Zhang(张宇青) and Youming Lei(雷佑铭). Logical stochastic resonance in a cross-bifurcation non-smooth system[J]. Chin. Phys. B, 2024, 33(3): 38201-038201.

参考文献

[1] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A 14 L453
[2] Nicolis C 1982 Tellus A 34 1
[3] Van der Sande G, Verschaffelt G, Danckaert J and Mirasso C R 2005 Phys. Rev. E 72 016113
[4] Duan L, Ren Y and Duan F 2022 Chaos, Solitons Fractals 162 112429
[5] Gabbiani F, Metzner W, Wessel R and Koch C 1996 Nature 384 564
[6] Narins P M 2001 Nature 410 644
[7] Zhang Y, Jin Y and Li Y 2021 Physica D 422 132908
[8] Zhang Y, Jin Y and Xu P 2020 Int. J. Mech. Sci. 172 105418
[9] Duan L, Duan F, Chapeau-Blondeau F and Abbott D 2020 Phys. Lett. A 384 126143
[10] Fu Y, Kang Y and Chen G 2020 Front. Comput. Neurosci. 14 24
[11] Liu X, Duan L, Duan F, Chapeau-Blondeau F and Abbott D 2021 Phys. Lett. A 403 127387
[12] Jin Y, Wang H, Xu P and Xie W 2023 Probab. Eng. Mech. 72 103418
[13] Zhai Y, Fu Y and Kang Y 2023 IEEE Trans. Instrum. Meas. 72 3508011
[14] Murali K, Sinha S, Ditto W L and Bulsara A R 2009 Phys. Rev. Lett. 102 104101
[15] Murali K, Rajamohamed I, Sinha S, Ditto W and Bulsara A 2009 Appl. Phys. Lett. 95 194102
[16] Zhang L, Song A and He J 2010 Phys. Rev. E 82 051106
[17] Xu Y, Jin X and Zhang H 2013 Phys. Rev. E 88 052721
[18] Cheng G, Liu W, Gui R and Yao Y 2020 Chaos, Solitons Fractals 131 109514
[19] Wu J, Xu Y and Ma S 2019 Chaos, Solitons Fractals 119 171
[20] Wang N and Song A 2014 Eur. Phys. J. B 87 117
[21] Dari A, Kia B, Bulsara A and Ditto W 2011 Chaos 21 047521
[22] Dari A, Kia B, Wang X, Bulsara A R and Ditto W 2011 Phys. Rev. E 83 041909
[23] Zhang L, Zheng W, Xie F and Song A 2017 Phys. Rev. E 96 052203
[24] Wang N and Song A 2015 Neurocomputing 155 80
[25] Sharma A, Kohar V, Shrimali M D and Sinha S 2014 Nonlinear Dyn. 76 431
[26] Cheng G, Zheng S, Dong J, Xu Z and Gui R 2021 Chaos 31 053105
[27] Gui R, Li J, Yao Y and Cheng G 2021 Chaos, Solitons Fractals 148 111043
[28] Aravind M, Murali K and Sinha S 2018 Phys. Lett. A 382 1581
[29] Gupta A, Sohane A, Kohar V, Murali K and Sinha S 2011 Phys. Rev. E 84 055201
[30] Yao Y, Cheng G and Gui R 2020 Chaos 30 073125
[31] Huang S, Yang J, Liu H and Sanjuán M 2021 Int. J. Bifurcation Chaos 31 2150246
[32] Storni R, Ando H, Aihara K, Murali K and Sinha S 2012 Phys. Lett. A 376 930
[33] Zhang H, Xu Y, Xu W and Li X 2012 Chaos 22 043130
[34] Zhang H, Yang T, Xu W and Xu Y 2014 Nonlinear Dyn. 76 649
[35] Lu S, Dai Z, Liu Y, Liu G, Yang H and Wang F 2019 Chin. J. Phys. 58 179
[36] Liao Z, Ma K, Shamim Sarker M, Yamahara H, Seki M and Tabata H 2022 Results Phys. 42 105968
[37] Kang Y, Xu J and Xie Y 2003 Acta Phys. Sin. 52 2712 (in Chinese)
[38] Nicolis C and Nicolis G 2017 Phys. Rev. E 95 032219
[39] Lei Y, Bi H and Zhang H 2018 Chaos 28 073104
[40] Bi H, Lei Y and Han Y 2019 Physica A 525 1296
[41] Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A 26 1589
[42] Cao L, Wu D and Ke S 1995 Phys. Rev. E 52 3228
[43] Liang G, Cao L and Wu D 2002 Phys. Lett. A 294 190

Logical stochastic resonance in a cross-bifurcation non-smooth system

Logical stochastic resonance in a cross-bifurcation non-smooth system

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]	Xian-Jun Wang(王宪军), Hua-Guang Gu(古华光), Yan-Bing Jia(贾雁兵), Bo Lu(陆博), and Hui Zhou(周辉). Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease[J]. 中国物理B, 2023, 32(9): 90502-090502.
[2]	Yong-Ge Yang(杨勇歌), Yun Meng(孟运), Yuan-Hui Zeng(曾远辉), and Ya-Hui Sun(孙亚辉). Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise[J]. 中国物理B, 2023, 32(9): 90201-090201.
[3]	Yun Zhai(翟云), Jinghua Xiao(肖井华), and Zhigang Zheng(郑志刚). Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling[J]. 中国物理B, 2023, 32(6): 60505-060505.
[4]	Lian Jia(贾莲), Chengwei Dong(董成伟), Hantao Li(李瀚涛), and Xiaohong Sui(眭晓红). Unstable periodic orbits analysis in the Qi system[J]. 中国物理B, 2023, 32(4): 40502-040502.
[5]	Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.
[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]	Wei Du(杜威), Kao Jia(贾考), Zhi-Long Shi(施志龙), and Lin-Ru Nie(聂林如). Current bifurcation, reversals and multiple mobility transitions of dipole in alternating electric fields[J]. 中国物理B, 2023, 32(2): 20505-020505.
[8]	Min-Yuan Liu(刘敏远), Hui Xu(许慧), and Zeng-Gui Wang(王增桂). Exact solutions of a time-fractional modified KdV equation via bifurcation analysis[J]. 中国物理B, 2023, 32(12): 120204-120204.
[9]	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.
[10]	Xueyi Guan(管学义), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior[J]. 中国物理B, 2022, 31(7): 70507-070507.
[11]	Li-Ping Zhang(张丽萍), Yang Liu(刘洋), Zhou-Chao Wei(魏周超), Hai-Bo Jiang(姜海波), Wei-Peng Lyu(吕伟鹏), and Qin-Sheng Bi(毕勤胜). Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor[J]. 中国物理B, 2022, 31(10): 100503-100503.
[12]	Xiao-Feng Shi(石晓峰), Dong-Jun Ma(马东军), Zong-Qiang Ma(马宗强), De-Jun Sun(孙德军), and Pei Wang(王裴). Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile[J]. 中国物理B, 2021, 30(9): 90201-090201.
[13]	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.
[14]	Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶). Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns[J]. 中国物理B, 2021, 30(5): 50502-050502.
[15]	Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Stabilization strategy of a car-following model with multiple time delays of the drivers[J]. 中国物理B, 2021, 30(12): 120506-120506.