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忆阻器可以用来模拟生物神经突触和描述电磁感应效应. 为了探索电磁感应作用下异构神经网络的动力学行为, 本文首先使用双局部有源忆阻器耦合一个Hindmarsh-Rose (HR)和两个FitzHugh-Nagumo (FN)神经元, 构成忆阻电磁感应下分数阶异构神经网络. 然后利用相图、分岔图、李雅普诺夫指数谱和吸引盆等动力学分析方法, 对该网络进行数值研究. 结果表明该神经网络表现出丰富的动力学行为, 包括共存行为、反单调现象、瞬态混沌和放电行为等, 为研究人脑放电行为提供支持, 随后进一步利用时间反馈控制方法实现了双稳态的控制. 最后, 在嵌入式硬件平台上实现了该神经网络, 验证了仿真结果的有效性.The dynamic behaviors of coupled neurons with different mathematical representations have received more and more attention in recent years. The coupling among heterogeneous neurons can show richer dynamic phenomena, which is of great significance in understanding the function of the human brain. In this paper, we present a fraction-order heterogeneous network with three neurons, which is built by coupling an FN neuron with two HR neurons. Complex electromagnetic surroundings have meaningful physical influence on the electrical activities of neurons. To imitate the effects of electromagnetic induction on the three-neuron heterogeneous network, we introduce a fraction-order locally active memristor in the neural network. The characteristics of this memristor are carefully analyzed by pinched hysteresis loops and its locally active characteristic is proved by the power-off plot and the DC v-i plot. Then, the parameter-dependent dynamic activities are investigated numerically by using several dynamical analysis methods, such as the phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, and attraction basins. In addition, the network also reveals rich dynamic behaviors, including coexisting activities, anti-monotonicity phenomena, transient chaos and firing patterns, providing support for further investigating the firing patterns of the human brain. In particular, complex dynamics, including coexisting attractors, anti-monotonicity, and firing patterns, can be influenced by the order and strength of electrical synaptic coupling and electromagnetic induction. The control of the bistable state can be realized through the time feedback control method, so that the bistable state can be transformed into an ideal monostable state. The study of the fraction-order memristive neural network may expand the field of view for understanding the collective behaviors of neurons. Finally, based on the ARM platform, we give a digital implementation of the fraction-order memristive neural network, which can verify the consistency with the numerical simulation results. In the future, we will explore more interesting memristive neural networks and study different types of methods to control the firing behaviors of the networks.
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Keywords:
- memristive electromagnetic induction /
- fraction-order neural network /
- attractor coexistence /
- anti-monotonicity
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[1] 周小荣, 罗晓曙, 蒋品群, 袁五届 2007 物理学报 56 5679Google Scholar
Zhou X R, Luo X S, Jing P Q, Yuan W J 2007 Acta Phys. Sin. 56 5679Google Scholar
[2] Xu Y, Jia Y, Ge M Y, Lu L L, Yang L J, Zhan X 2018 Neurocomputing 283 196Google Scholar
[3] Izhikevich E M 2003 IEEE Trans. Neural Netw. 14 1569Google Scholar
[4] Bao B C, Yang Q, Zhu L, Bao H 2019 Int. J. Bifurc. Chaos 29 1930010Google Scholar
[5] Hindmarsh J L, Rose R M 1982 Nature 296 5853Google Scholar
[6] Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond, Ser B: Biol. Sci. 221 87Google Scholar
[7] Izhikevich E M, Fitzhugh R 2006 Scholarpedia 1 1349Google Scholar
[8] Chay T R 1985 Physica D 16 233Google Scholar
[9] Xu Q, Liu T, Feng C T, Bao H, Wu H G, Bao B C 2021 Chin. Phys. B 30 128702Google Scholar
[10] Li Z J, Zhou H Y, Wang M J, Ma M L 2021 Nonlinear Dyn. 104 1455Google Scholar
[11] Ding D W, Jiang L, Hu Y B, Yang Z L, Li Q 2021 Chaos 31 083107Google Scholar
[12] Njitacke Z T, Awrejcewicz J, Ramakrishnan B, Rajagopal K, Kengne J 2022 Nonlinear Dyn. 107 2867Google Scholar
[13] De S, Balakrishnan J 2020 Commun. Nonlinear Sci. Numer. Simul. 90 105391Google Scholar
[14] 孙晓娟, 杨白桦, 吴晔, 肖井华 2014 物理学报 63 120502Google Scholar
Sun X J, Yang B H, Wu Y, Xiao J H 2014 Acta Phys. Sin. 63 120502Google Scholar
[15] 丁学利, 古华光, 贾冰, 李玉叶 2021 物理学报 70 218701Google Scholar
Ding X L, Gu H G, Jia B, Li Y Y 2021 Acta Phys. Sin. 70 218701Google Scholar
[16] 吴莹, 徐健学, 何岱海, 靳伍银 2005 物理学报 54 3457Google Scholar
Wu Y, Xu J X, He D H, Jin W Y 2005 Acta Phys. Sin. 54 3457Google Scholar
[17] Lv M, Ma J, Yao Y G, Alzahrani F 2019 Sci. China-Technol. Sci. 62 448Google Scholar
[18] Hu X Y, Liu C X, Liu L, Ni J K, Yao Y P 2018 Nonlinear Dyn. 91 1541Google Scholar
[19] Wan Q Z, Yan Z D, Li F, Chen S M, Liu J 2022 Chaos 32 073107Google Scholar
[20] Lin H R, Wang C H, Hong Q H, Sun Y C 2020 IEEE Trans. Circuits Syst. II-Express Briefs 67 3472Google Scholar
[21] Li C L, Li H D, Xie W W, Du J R 2021 Nonlinear Dyn. 106 1041Google Scholar
[22] Yu F, Zhang Z N, Shen H, Huang Y Y, Cai S, Du S C 2022 Chin. Phys. B 31 020505Google Scholar
[23] 罗佳, 孙亮, 乔印虎 2022 计算物理 39 109Google Scholar
Luo J, Sun L, Qiao Y H 2022 Chin. J. Comput. Phys. 39 109Google Scholar
[24] Xu Q, Ju Z T, Ding S K, Feng C T, Chen M, Bao B C 2022 Cogn. Neurodyn. 16 1221Google Scholar
[25] Bao H, Hu A H, Liu W B, Bao B C 2020 IEEE Trans. Neural Netw. Learn. Syst. 31 502Google Scholar
[26] Bao H, Liu W B, Hu A H 2019 Nonlinear Dyn. 95 43Google Scholar
[27] Tenreiro Machado J, Duarte F B, Duarte G M, 2012 Int. J. Bifurcat. Chaos 22 1250249Google Scholar
[28] Tenreiro Machado J A, Lopes A M 2016 Nonlinear Dyn. 86 1613Google Scholar
[29] Tzounas G, Dassios I, Murad M A A, Milano F 2020 IEEE Trans. Power Syst. 35 4622Google Scholar
[30] Kërçi T, Giraldo J, Milano F 2020 Int. J. Elec. Power 119 105819Google Scholar
[31] Chen L, He Z L, Li C D, Wen S P, Chen Y R 2020 Int. J. Bifurcat. Chaos 30 2050172Google Scholar
[32] Jahanshahi H, Yousefpour A, Munoz-Pacheco J M, Kacar S, Viet-Thanh P, Alsaadi F E 2020 Appl. Math. Comput. 383 125310Google Scholar
[33] Dong J, Zhang G J, Xie Y, Yao H, Wang J 2014 Cogn. Neurodyn. 8 167Google Scholar
[34] Wu G C, Baleanu D 2015 Commun. Nonlinear Sci. Numer. Simul. 22 95Google Scholar
[35] Lin H R, Wang C H, Sun Y C, Yao W 2020 Nonlinear Dyn. 100 3667Google Scholar
[36] Chua L 2013 Nanotechnology 24 383001Google Scholar
[37] Chua L 2015 Radioengineering 24 319Google Scholar
[38] Weiher M, Herzig M, Tetzlaff R, Ascoli A, Mikolajick T, Slesazeck S 2019 IEEE Trans. Circuits Syst. I-Regul 66 2627Google Scholar
[39] Yu H, Du S Z, Dong E Z, Tong J G 2022 Chaos Solitons Fractals 160 112220Google Scholar
[40] Li C B, Wang X, Chen G R 2017 Nonlinear Dyn. 90 1335Google Scholar
[41] Li C B, Sprott J C, Hu W, Xu Y J 2017 Int. J. Bifurcat. Chaos 27 1750160Google Scholar
[42] Park J H, Huh S H, Kim S H, Seo S J, Park G T 2005 IEEE Trans. Neural Netw. 16 414Google Scholar
[43] Yadav K, Prasad A, Shrimali M D 2018 Phys. Lett. A 382 2127Google Scholar
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