Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

doi:10.1088/1674-1056/ad1483

Abstract The brain is a complex network system in which a large number of neurons are widely connected to each other and transmit signals to each other. The memory characteristic of memristors makes them suitable for simulating neuronal synapses with plasticity. In this paper, a memristor is used to simulate a synapse, a discrete small-world neuronal network is constructed based on Rulkov neurons and its dynamical behavior is explored. We explore the influence of system parameters on the dynamical behaviors of the discrete small-world network, and the system shows a variety of firing patterns such as spiking firing and triangular burst firing when the neuronal parameter α is changed. The results of a numerical simulation based on Matlab show that the network topology can affect the synchronous firing behavior of the neuronal network, and the higher the reconnection probability and number of the nearest neurons, the more significant the synchronization state of the neurons. In addition, by increasing the coupling strength of memristor synapses, synchronization performance is promoted. The results of this paper can boost research into complex neuronal networks coupled with memristor synapses and further promote the development of neuroscience.

Keywords: small-world networks Rulkov neurons memristor synchronization

Received: 21 October 2023
Revised: 29 November 2023
Accepted manuscript online: 12 December 2023

PACS:	87.19.ll	(Models of single neurons and networks)
	87.19.lj	(Neuronal network dynamics)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by the Key Projects of Hunan Provincial Department of Education (Grant No. 23A0133), the Natural Science Foundation of Hunan Province (Grant No. 2022JJ30572), and the National Natural Science Foundations of China (Grant No. 62171401).

Corresponding Authors: Minglin Ma
E-mail: minglin_ma@xtu.edu.cn

Cite this article:

Jieyu Lu(鲁婕妤), Xiaohua Xie(谢小华), Yaping Lu(卢亚平), Yalian Wu(吴亚联), Chunlai Li(李春来), and Minglin Ma(马铭磷) Dynamical behaviors in discrete memristor-coupled small-world neuronal networks 2024 Chin. Phys. B 33 048701

[1] Li Y Y, Wei Z C, Zhang W, Perc M and Repnik R 2019 Appl. Mat. Compu. 354 180
[2] Xie Y, Xu Y and Ma J 2023 Nonlinear Dyn. 111 11521
[3] Njitacke Z T, Parthasarathy S, Takembo C N, RajagopalK and Awrejcewicz J 2023 Eur. Phy. J. 138 473
[4] Almatroud A O 2021 Fractal Fract. 5 20
[5] Tabekoueng Z N, Sriram, Rajagopal K, Karthikeyan A and Awrejcewicz Z 2023 Chaos 33 063153
[6] Muni S S 2023 Phy. Scr. 98 085205
[7] Xu Y Y, Li H L, Zhang L, Hu C and Jiang H J 2023 Neural Processing Lett. 55 6657
[8] Chen C J, Min F H, Zhang Y Z and Bao H 2023 Chaos Solitons Fractals 167 113068
[9] Ramadoss and Janarthanan 2023 Eur. Phys. J. Plus 138 962
[100] Ma M L and Lu Y P 2023 Chaos Solitons Fractals 172 113518
[12] Ren J, Mou J, Banerjee and Zhang Y S 2023 Chaos Solitons Fractals 167 113024
[13] Sun Q K, He S B, Sun K H, Wang H H 2022 Chin. Phys. B 31 120501
[14] Almatroud O A and Pham V 2023 Math 11 1319
[15] Almatroud O A, Pham V, Grassi G, Alshammari M, Albosaily S and Huynh V V 2023 Math 11 3725
[16] Li H D, Li L and Du R 2023 Nonlinear Dyn. 111 2895
[17] Wang M J and Gu F 2023 Chin. Phys. B 33 020504
[18] Almatroud O A, Hioual A, Ouannas A, Sawalha M M, Alshammari S and Alshammari M 2023 Fractal Fract. 7 118
[19] Zhou S, Qiu Y, Wang X and Zhang Y 2023 Nonlinear Dyn. 111 9571
[20] Li Z J and Chen J 2023 Chaos Solitons Fractals 175 114017
[21] Wan Q Z, Li F, Chen S M and Yang Q 2023 Chaos Solitons Fractals 169 113259
[22] Chen W B, Song L K, Wang S B, Zhang Z Y, Wang G Y, Hu G H and Gao S 2023 Adv. Electron. Mater. 9 2200833
[23] Ma M L, Xie X H, Yang Y, Li Z J and Sun Y C 2023 Chin. Phys. B 32 058701
[24] Ding S K, Wang N, Bao H, Wu H G and Xu Q 2023 Chaos Solitons Fractals 166 112899
[25] Lu Y C, Li H M and Li C L 2023 Neurocomputin. 544 126246
[26] Wang M J, Peng J W, Zhang X N, Lu H H C and Li Z J 2023 Nonlinear Dyn. 111 15397
[27] Peng C, Li Z J, Wang M J and Ma M J 2023 Nonlinear Dyn.
[28] Ma M L, Xiong K L, Li Z J and He S B 2023 Chin. Phys. B 33 028706
[29] Deng Z K, Wang C H, Lin H R and Sun Y C 2022 IEEE Trans. Comput-Aided Des. Integr. Circuits Syst. 42 2604
[30] Peng Y X, He S B and Sun K H 2022 Nonlinear Dyn. 107 1263
[31] Kong X X, Yu F, Yao W, Cai S, Zhang J and Lin H R 2024 Neural Networks 171 85
[32] Yu F, Shen H, Yu Q L, Kong X X, Sharma P K and Cai S 2022 IEEE Trans Netw Sci Eng. 10 845
[101] Tang D, Wang C H, Lin H R and Fei Y 2024 Nonlinear Dyn. 112 1511
[33] He S B, Liu J, Wang H H and Sun K H 2023 Neurocomputing. 523 1
[34] Lai Q, Wan Z Q, Zhang H and Chen G R 2022 IEEE Trans Neural Netw Learn Syst. 34 7824
[35] Lai Q, Yang L and Liu Y 2022 Chaos Solitons Fractals 165 112781
[36] Lai Q, Lai C, Zhang H and Li C B 2022 Chaos Solitons Fractals 158 112017
[37] Sun J W, Wang Y Y, Liu P, Wen S P and Wang Y F 2023 IEEE Internet Things J. 10 16332
[38] Ma M L, Lu Y P, Li Z J, Sun Y C and Wang C H 2023 Fractal Fract. 7 82
[39] Rulkov N F 2001 Phys Rev Lett. 86 183

[1]	Dynamics and synchronization of neural models with memristive membranes under energy coupling Jingyue Wan(万婧玥), Fuqiang Wu(吴富强), Jun Ma(马军), and Wenshuai Wang(汪文帅). Chin. Phys. B, 2024, 33(5): 050504.
[2]	Synchronization and firing mode transition of two neurons in a bilateral auditory system driven by a high--low frequency signal Charles Omotomide Apata, Yi-Rui Tang(唐浥瑞), Yi-Fan Zhou(周祎凡), Long Jiang(蒋龙), and Qi-Ming Pei(裴启明). Chin. Phys. B, 2024, 33(5): 058704.
[3]	Chimera states of phase oscillator populations with nonlocal higher-order couplings Yonggang Wu(伍勇刚), Huajian Yu(余华健), Zhigang Zheng(郑志刚), and Can Xu(徐灿). Chin. Phys. B, 2024, 33(4): 040504.
[4]	Dynamics analysis and cryptographic implementation of a fractional-order memristive cellular neural network model Xinwei Zhou(周新卫), Donghua Jiang(蒋东华), Jean De Dieu Nkapkop, Musheer Ahmad, Jules Tagne Fossi, Nestor Tsafack, and Jianhua Wu(吴建华). Chin. Phys. B, 2024, 33(4): 040506.
[5]	Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption Xiaoxia Li(李晓霞), Qianqian He(何倩倩), Tianyi Yu(余天意),Zhuang Cai(才壮), and Guizhi Xu(徐桂芝). Chin. Phys. B, 2024, 33(3): 030505.
[6]	Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk Minglin Ma(马铭磷), Kangling Xiong(熊康灵), Zhijun Li(李志军), and Shaobo He(贺少波). Chin. Phys. B, 2024, 33(2): 028706.
[7]	Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise Xun Yan(晏询), Zhijun Li(李志军), and Chunlai Li(李春来). Chin. Phys. B, 2024, 33(2): 028705.
[8]	Quantum synchronization with correlated baths Lei Li(李磊), Chun-Hui Wang(王春辉), Hong-Hao Yin(尹洪浩), Ru-Quan Wang(王如泉), and Wu-Ming Liu(刘伍明). Chin. Phys. B, 2024, 33(2): 020306.
[9]	A step to the decentralized real-time timekeeping network Fangmin Wang(王芳敏), Yufeng Chen(陈雨锋), Jianhua Zhou(周建华), Yuting Lin(蔺玉亭), Jun Yang(杨军), Bo Wang(王波), and Lijun Wang(王力军). Chin. Phys. B, 2024, 33(1): 010702.
[10]	Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization Xue-Li Ding(丁学利), Hua-Guang Gu(古华光), Yu-Ye Li(李玉叶), and Yan-Bing Jia(贾雁兵). Chin. Phys. B, 2023, 32(8): 088701.
[11]	Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor Yi-Qun Li(李逸群), Jian Liu(刘坚), Chun-Biao Li(李春彪), Zhi-Feng Hao(郝志峰), and Xiao-Tong Zhang(张晓彤). Chin. Phys. B, 2023, 32(8): 080503.
[12]	Lightweight and highly robust memristor-based hybrid neural networks for electroencephalogram signal processing Peiwen Tong(童霈文), Hui Xu(徐晖), Yi Sun(孙毅), Yongzhou Wang(汪泳州), Jie Peng(彭杰),Cen Liao(廖岑), Wei Wang(王伟), and Qingjiang Li(李清江). Chin. Phys. B, 2023, 32(7): 078505.
[13]	Stability and multistability of synchronization in networks of coupled phase oscillators Yun Zhai(翟云), Xuan Wang(王璇), Jinghua Xiao(肖井华), and Zhigang Zheng(郑志刚). Chin. Phys. B, 2023, 32(6): 060503.
[14]	Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling Yun Zhai(翟云), Jinghua Xiao(肖井华), and Zhigang Zheng(郑志刚). Chin. Phys. B, 2023, 32(6): 060505.
[15]	A progressive surrogate gradient learning for memristive spiking neural network Shu Wang(王姝), Tao Chen(陈涛), Yu Gong(龚钰), Fan Sun(孙帆), Si-Yuan Shen(申思远), Shu-Kai Duan(段书凯), and Li-Dan Wang(王丽丹). Chin. Phys. B, 2023, 32(6): 068704.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamical behaviors in discrete memristor-coupled small-world neuronal networks

Cite this article:

Online attention