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
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.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12072262) and the Shaanxi Computer Society & Xiangteng Company Foundation.
Corresponding Authors:
Youming Lei
E-mail: leiyouming@nwpu.edu.cn
Cite this article:
Yuqing Zhang(张宇青) and Youming Lei(雷佑铭) Logical stochastic resonance in a cross-bifurcation non-smooth system 2024 Chin. Phys. B 33 038201
[1] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A14 L453 [2] Nicolis C 1982 Tellus A34 1 [3] Van der Sande G, Verschaffelt G, Danckaert J and Mirasso C R 2005 Phys. Rev. E72 016113 [4] Duan L, Ren Y and Duan F 2022 Chaos, Solitons Fractals162 112429 [5] Gabbiani F, Metzner W, Wessel R and Koch C 1996 Nature384 564 [6] Narins P M 2001 Nature410 644 [7] Zhang Y, Jin Y and Li Y 2021 Physica D422 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. A384 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. A403 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. E82 051106 [17] Xu Y, Jin X and Zhang H 2013 Phys. Rev. E88 052721 [18] Cheng G, Liu W, Gui R and Yao Y 2020 Chaos, Solitons Fractals131 109514 [19] Wu J, Xu Y and Ma S 2019 Chaos, Solitons Fractals119 171 [20] Wang N and Song A 2014 Eur. Phys. J. B87 117 [21] Dari A, Kia B, Bulsara A and Ditto W 2011 Chaos21 047521 [22] Dari A, Kia B, Wang X, Bulsara A R and Ditto W 2011 Phys. Rev. E83 041909 [23] Zhang L, Zheng W, Xie F and Song A 2017 Phys. Rev. E96 052203 [24] Wang N and Song A 2015 Neurocomputing155 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 Chaos31 053105 [27] Gui R, Li J, Yao Y and Cheng G 2021 Chaos, Solitons Fractals148 111043 [28] Aravind M, Murali K and Sinha S 2018 Phys. Lett. A382 1581 [29] Gupta A, Sohane A, Kohar V, Murali K and Sinha S 2011 Phys. Rev. E84 055201 [30] Yao Y, Cheng G and Gui R 2020 Chaos30 073125 [31] Huang S, Yang J, Liu H and Sanjuán M 2021 Int. J. Bifurcation Chaos31 2150246 [32] Storni R, Ando H, Aihara K, Murali K and Sinha S 2012 Phys. Lett. A376 930 [33] Zhang H, Xu Y, Xu W and Li X 2012 Chaos22 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. E95 032219 [39] Lei Y, Bi H and Zhang H 2018 Chaos28 073104 [40] Bi H, Lei Y and Han Y 2019 Physica A525 1296 [41] Sancho J M, San Miguel M, Katz S L and Gunton J D 1982 Phys. Rev. A26 1589 [42] Cao L, Wu D and Ke S 1995 Phys. Rev. E52 3228 [43] Liang G, Cao L and Wu D 2002 Phys. Lett. A294 190
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