Statistical complexity and stochastic resonance in bistable coupled network systems excited by non-Gaussian noise

doi:10.1088/1674-1056/adfef7

Abstract This study investigates stochastic resonance (SR) phenomena in bistable coupled networks driven by non-Gaussian noise. Employing signal-to-noise ratio (SNR) and statistical complexity as quantitative metrics, we characterize the SR behavior. First, the dimensionality of a coupled network system is reduced via the mean field theory. Subsequently, we derive closed-form analytical expressions of SNR by the path integral method, the slaving principle and the two-state model theory. Numerical simulations are used to validate the consistency between SR features identified through statistical complexity and those obtained via SNR calculations, thereby corroborating the reliability of our analytical framework. Both theoretical and numerical results conclusively demonstrate the occurrence of SR in the network system. Parametric analyses further elucidate the modulation of SR characteristics by three critical factors: non-Gaussian noise intensity parameters, noise correlation timescale and inter-node coupling strength. Finally, we explore the system’s size resonance properties.

Keywords: non-Gaussian noise bistable coupled network systems statistical complexity measure stochastic resonance

Received: 26 May 2025
Revised: 17 August 2025
Accepted manuscript online: 26 August 2025

PACS:	05.10.Gg	(Stochastic analysis methods)
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)

Fund: He Meijuan’s research was partially supported by the Key Project of the Gansu Natural Science Foundation (Grant Nos. 24JRRA226 and 23JRRA882), Lanzhou Youth Science and Technology Talent Innovation Project (Grant No. 2024-QN-179), the Foundation for Innovative Fundamental Research Group Project of Gansu Province, China (Grant No. 25JRRA805), the National Natural Science Foundation of China (Grant Nos. 11602184 and 62463016), the Industrial Support and Guidance Project of Colleges and Universities of Gansu Province (Grant No. 2024CYZC-23), and Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University.

Corresponding Authors: Meijuan He
E-mail: hemeijuan@mail.lzjtu.cn

Cite this article:

Meijuan He(何美娟), Lingyun Li(李凌云), Wantao Jia(贾万涛), and Jiangang Zhang(张建刚) Statistical complexity and stochastic resonance in bistable coupled network systems excited by non-Gaussian noise 2026 Chin. Phys. B 35 030501

[1] Dorogovtsev S N, Goltsev A V and Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[2] Geier C, Stender M and Hoffmann N 2024 J. Sound Vib. 590 118544
[3] Li L, Jiang W and Tu Z 2023 Appl. Math. Model 119 54
[4] Böttcher L and Porter M A 2024 Phys. Rev. E 109 024314
[5] Pikovsky A, Zaikin A and de La Casa M A 2002 Phys. Rev. Lett. 88 050601
[6] Holder A B, Zuparic M L and Kalloniatis A C 2017 Physica D 341 10
[7] Ji Y, Gong Y, Su S and Bai X 2021 Complexity 2021 6680287
[8] Liu Q, Xu Y, Xu C and Kurths J 2018 Appl. Math. Model 64 249
[9] Gong Y, Hao Y, Xie Y, Ma X and Yang C 2009 Biophys. Chem. 144 88
[10] JiaW, Feng X, HaoMand Ma S 2024 Chaos Soliton Fract. 185 115134
[11] Shi T T, Xu X M, Sun K H, Ding Y P and Huang G W 2020 Chin. Phys. B 29 050501
[12] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[13] Harikrishnan N B and Nagaraj N 2021 Neural Networks 143 425
[14] Liu D, Wu Y, Xu Y and Li J 2019 Mech. Syst. Signal Pr. 130 201
[15] Huang M L, Yang Y G and Liu Y 2024 Chin. Phys. B 33 060203
[16] Hang D, Ye J and Huang D 2025 Commun. Nonlinear Sci. 140 108354
[17] Lei Y, Han D, Lin J and He Z 2013 Mech. Syst. Signal Pr 38 113
[18] Jiang Z, Zhang G and Gao Y 2025 Appl. Math. Model 137 115657
[19] Douglass J K, Wilkens L, Pantazelou E and Moss F 1993 Nature 365 337
[20] Mato G 1999 Phys. Rev. E 59 3339
[21] Jiao S, Gao R, Xue Q and Shi J 2023 Chin. Phys. B 32 050202
[22] Dykman M I, Haken H, Hu G, Luchinsky D G, Mannella R, McClintock P, Ning C Z, Stein N D and Stocks N G 1993 Phys. Lett. A 180 332
[23] Guo X and Cao T 2022 Chin. J. Phys. 77 721
[24] Gammaitoni L, Hänggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[25] Krawiecki A and Kosiński R A 2020 Acta Phys. Pol. A 138 824
[26] Wang Y and He M 2022 Acta. Phys. Sin. 71 190501 (in Chinese)
[27] Guo F, Luo X, Li S and Zhou Y 2010 Chin. Phys. B 19 080502
[28] Rosso O and Masoller C 2009 Phys. Rev. E 79 040106
[29] He M, Xu W, Sun Z and Jia W 2013 Int. J. Dynam. Control. 1 254
[30] He M, Xu W, Sun Z and Du L 2015 Commun. Nonlinear Sci. Numer. Simul. 28 39
[31] Sun Z, Dang P and Xu W 2019 Chaos Soliton Fract. 125 34
[32] Guo Y, Ding J and Mi L 2024 Chaos Soliton Fract. 179 114380
[33] Kometani K and Shimizu H 1975 J. Stat. Phys. 13 473
[34] Pikovsky A, Rateitschak K and Kurths J 1994 Z. Physik B 95 541
[35] Øksendal B 2003 Stochastic Differential Equations: An Introduction with Applications (Berlin: Springer)
[36] Fuentes M A, Toral R and Wio H S 2001 Phys A 295 114
[37] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House)
[38] Zhu W and Cai G 2017 Introduction to stochastic dynamics (Beijing: Science Press)
[39] Cubero D 2008 Phys. Rev. E 77 021112
[40] Grifoni M and Hänggi P 1996 Phys. Rev. Lett. 76 1611

[1]	Probabilistic distribution and stochastic P-bifurcation of a nonlinear energy-regenerative suspension system with time-delayed feedback control Zhao-Bin Zeng(曾昭彬), Ya-Hui Sun(孙亚辉), and Yang Liu(刘洋). Chin. Phys. B, 2026, 35(1): 010201.
[2]	Adaptive multi-stable stochastic resonance assisted by neural network and physical supervision Xucan Li(李栩灿), Deming Nie(聂德明), Ming Xu(徐明), and Kai Zhang(张凯). Chin. Phys. B, 2025, 34(5): 050203.
[3]	Study and circuit design of stochastic resonance system based on memristor chaos induction Qi Liang(梁琦), Wen-Xin Yu(于文新), and Qiu-Mei Xiao(肖求美). Chin. Phys. B, 2025, 34(4): 040502.
[4]	Dynamic properties of rumor propagation model induced by Lévy noise on social networks Ying Jing(景颖), Youguo Wang(王友国), Qiqing Zhai(翟其清), and Xianli Sun(孙先莉). Chin. Phys. B, 2024, 33(9): 090203.
[5]	Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control Mei-Ling Huang(黄美玲), Yong-Ge Yang(杨勇歌), and Yang Liu(刘洋). Chin. Phys. B, 2024, 33(6): 060203.
[6]	Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system Ling Xu(徐玲) and Lei Jiang(姜磊). Chin. Phys. B, 2024, 33(6): 060503.
[7]	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.
[8]	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.
[9]	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). Chin. Phys. B, 2024, 33(1): 010501.
[10]	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.
[11]	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.
[12]	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.
[13]	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.
[14]	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.
[15]	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.

[1]	ZHAO MING-XIN (赵明信), WANG SHENG-LIE (汪盛烈), SUN XIAN-PING (孙献平), LI LI-YUN (李丽云), ZENG XI-ZHI (曾锡之). MEASUREMENTS OF ¹²⁹Xe NUCLEAR MAGNETIC RESONANCE IN GASEOUS, LIQUID AND SOLID XENON[J]. Acta Physica Sinica (Overseas Edition), 1994, 3(7): 501 -505 .
[2]	WANG XIAO-GUANG (王晓光), SUN CHANG-PU (孙昌璞). HIGHER-ORDER CORRECTION FOR ROTATING WAVE APPROXIMATION, RABI TRANSFORMATION, AND ITS APPLICATIONS IN THE JAYNES-CUMMINGS MODEL[J]. Acta Physica Sinica (Overseas Edition), 1996, 5(12): 881 -889 .
[3]	Hou Bang-Pin (侯邦品), Liu Jie (刘杰), Hu Ping (胡萍). Sum and two-atom dipole squeezing in a system of a two-mode vacuum field interacting with two coupled atoms[J]. Chinese Physics, 2002, 11(1): 30 -34 .
[4]	Sun Li-Qun (孙利群), Wang Jia (王佳), Hong Tao (洪涛), Tian Qian (田芊). A virtual optical probe based on evanescent wave interference[J]. Chinese Physics, 2002, 11(10): 1022 -1027 .
[5]	Chen Shi-Hua (陈士华), Liu Jie (刘杰), Xie Jin (谢进), Lu Jun-An (陆君安). Tracking control and synchronization of chaotic systems based upon sampled-data feedback[J]. Chinese Physics, 2002, 11(3): 233 -237 .
[6]	Yao Ming-Zhen (姚明珍), Gu Mu (顾牡), Liu Feng-Song (刘峰松). Theoretical study on defects associated with lead vacancies in PbWO₂ crystals[J]. Chinese Physics, 2003, 12(1): 84 -88 .
[7]	Zhang Bai-Gang (张百钢), Yao Jian-Quan (姚建铨), Ding Xin (丁欣), Zhang Hao (张浩), Wang Peng (王鹏), Xu De-Gang (徐德刚), Yu Guo-Jun (禹国俊), Zhang Fan (张帆). Low-threshold, high-efficiency, high-repetition-rate optical parametric generator based on periodically poled LiNbO₃[J]. Chinese Physics, 2004, 13(3): 364 -368 .
[8]	Sun Jian-Min (孙建敏), Zhong Zhi-Ping (钟志萍), Zhu Lin-Fan (朱林繁), Liu Xiao-Jing (刘小井), Yuan Zhen-Sheng (苑震生), Xu Ke-Zun (徐克尊). Absolute oscillator strength densities below 100eV of N₂[J]. Chinese Physics, 2005, 14(7): 1378 -1381 .
[9]	Cao Quan-Jun(曹全君), Zhang Yi-Men(张义门), Zhang Yu-Ming(张玉明), Lü Hong-Liana(吕红亮), Wang Yue-Hu(王悦湖), Chang Yuan-Cheng(常远程), and Tang Xiao-Yan(汤晓燕). A CAD oriented quasi-analytical large-signal drain current model for 4H-SiC MESFETs[J]. Chinese Physics, 2007, 16(4): 1097 -1100 .
[10]	Gao Fei(高飞), Li Zhuo-Qiu(李卓球), and Tong Heng-Qing(童恒庆). Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization[J]. Chin. Phys. B, 2008, 17(4): 1196 -1201 .

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Statistical complexity and stochastic resonance in bistable coupled network systems excited by non-Gaussian noise

Cite this article:

Online attention