Abstract: Biological neurons can be excited to maintain certain firing patterns following different external stimuli, and similar changes in electrical activities can be reproduced in some neural circuits by applying an external voltage. Generic neural circuits are composed of capacitors, induction coils, resistors, and nonlinear resistors, and continuous energy exchange between the capacitive and inductive components is crucial for preserving output voltages. Incorporating nonlinear elements causes interactions between the charge flow across the capacitor and the induced electromotive force on the inductor. It is a challenge to explore the occurrence of nonlinear oscillation and coherence resonance in a neural circuit without using a capacitor and nonlinear resistor, and it considers the case lack of electric field energy. In this paper, a simple neural circuit is proposed that combines two inductors, one magnetic flux-controlled memristor (MFCM), and three resistors, with two constant voltage sources in the branch circuits used as reverse potentials in the ion channels. The field energy has an exact form, and it is stored in the circuit components as a magnetic field. Scale transformation is applied on the circuit equations and field energy function to obtain equivalent dimensionless forms of the memristive neuron and Hamilton energy. The reference values for the physical time and capacitance are represented by an appropriate combination of resistance and inductance, because the capacitance value is unavailable. The memristive neuron without capacitive effect still shows similar firing patterns, and coherence resonance is induced under noisy excitation. The emergence of coherence resonance can be predicted by calculating the distribution of the average energy <H> versus noise intensity, and the value for <H> reaches a maximum under coherence resonance. Finally, an adaptive law for parameter growth under energy control is proposed to control mode transitions in the electrical activity. The methodology and results of this work offer insights into the oscillatory mechanism of neural circuits, and showcase how magnetic field control can be used to manage neural activations.

持续的磁场能量交换维系忆阻神经元的放电

[1]AltanMA, OrmanK, BabacanY, et al., 2024. Special memristor and memristor-based compact neuron circuit. Journal of Circuits, Systems and Computers, 33(5):2450091.

[2]AscoliA, CorintoF, 2013. Memristor models in a chaotic neural circuit. International Journal of Bifurcation and Chaos, 23(3):1350052.

[3]BabacanY, KaçarF, GürkanK, 2016. A spiking and bursting neuron circuit based on memristor. Neurocomputing, 203:86-91.

[4]BrüttM, KaernbachC, 2021. On the role of the excitation/inhibition balance of homeostatic artificial neural networks. Entropy, 23(12):1681.

[5]BuzsákiG, DraguhnA, 2004. Neuronal oscillations in cortical networks. Science, 304(5679):1926-1929.

[6]ChenL, LiXL, TjiaM, et al., 2022. Homeostatic plasticity and excitation-inhibition balance: the good, the bad, and the ugly. Current Opinion in Neurobiology, 75:102553.

[7]ChenZQ, TangH, WangZL, et al., 2015. Design and circuit implementation for a novel charge-controlled chaotic memristor system. Journal of Applied Analysis & Computation, 5(2):251-261.

[8]ChengS, WangNG, ArnoldDP, 2007. Modeling of magnetic vibrational energy. harvesters using equivalent circuit representations. Journal of Micromechanics and Microengineering, 17(11):2328.

[9]ChuaL, 1971. Memristor–the missing circuit element. IEEE Transactions on Circuit Theory, 18(5):507-519.

[10]DagarS, ChowdhurySR, BapiRS, et al., 2016. Near-infrared spectroscopy-electroencephalography-based brain-state-dependent electrotherapy: a computational approach based on excitation-inhibition balance hypothesis. Frontiers in Neurology, 7:123.

[11]DouglasRJ, MartinKAC, 2004. Neuronal circuits of the neocortex. Annual Review of Neuroscience, 27:419-451.

[12]DuSC, DengQ, HongQH, et al., 2022. A memristor-based circuit design and implementation for blocking on Pavlov associative memory. Neural Computing and Applications, 34(17):14745-14761.

[13]FroemkeRC, MerzenichMM, SchreinerCE, 2007. A synaptic memory trace for cortical receptive field plasticity. Nature, 450(7168):425-429.

[14]GaoR, PetersonEJ, VoytekB, 2017. Inferring synaptic excitation/inhibition balance from field potentials. NeuroImage, 158:70-78.

[15]GraasEL, BrownEA, LeeRH, 2004. An FPGA-based approach to high-speed simulation of conductance-based neuron models. Neuroinformatics, 2(4):417-435.

[16]GuoYT, MaJ, 2025. An electromechanical arm model controlled by artificial muscles. Science China Technological Sciences, 68(4):1420403.

[17]GuoYT, MaJ, ZhangXF, et al., 2024. Memristive oscillator to memristive map, energy characteristic. Science China Technological Sciences, 67(5):1567-1578.

[18]HouS, WangHD, FanDG, et al., 2024. The effects of negative regulation on the dynamical transition in epileptic network. International Journal of Bifurcation and Chaos, 34(3):2450038.

[19]IndiveriG, Linares-BarrancoB, HamiltonTJ, et al., 2011. Neuromorphic silicon neuron circuits. Frontiers in Neuroscience, 5:73.

[20]IsaacJTR, CrairMC, NicollRA, et al., 1997. Silent synapses during development of thalamocortical inputs. Neuron, 18(2):269-280.

[21]IzhikevichEM, 2006. Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting. MIT Press, Cambridge, Massachusetts, USA.

[22]JiaJE, WangCN, ZhangXF, et al., 2024. Energy and self-adaption in a memristive map neuron. Chaos, Solitons & Fractals, 182:114738.

[23]JiaJN, YangFF, MaJ, 2023. A bimembrane neuron for computational neuroscience. Chaos, Solitons & Fractals, 173:113689.

[24]JiaJN, XieY, WangCN, et al., 2024. Thermosensitive double-membrane neurons and their network dynamics. Physica Scripta, 99(11):115030.

[25]KatzLC, ShatzCJ, 1996. Synaptic activity and the construction of cortical circuits. Science, 274(5290):1133-1138.

[26]KirischukS, 2022. Keeping excitation‍–inhibition ratio in balance. International Journal of Molecular Sciences, 23(10):5746.

[27]LeiZ, MaJ, 2025. Coherence resonance and energy dynamics in a memristive map neuron. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(2):023158.

[28]LiCL, YangYY, DuJR, et al., 2021. A simple chaotic circuit with magnetic flux-controlled memristor. The European Physical Journal Special Topics, 230(7):1723-1736.

[29]LiSQ, LiuZ, ZhaoH, et al., 2016. Wireless power transfer by electric field resonance and its application in dynamic charging. IEEE Transactions on Industrial Electronics, 63(10):6602-6612.

[30]LiZJ, ChenKJ, 2023. Neuromorphic behaviors in a neuron circuit based on current-controlled Chua corsage memristor. Chaos, Solitons & Fractals, 175:114017.

[31]LiuF, LiHY, HuW, et al., 2024. Review of neural network model acceleration techniques based on FPGA platforms. Neurocomputing, 610:128511.

[32]MaJ, 2023. Biophysical neurons, energy, and synapse controllability: a review. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 24(2):109-129.

[33]MaJ, YangZQ, YangLJ, et al., 2019. A physical view of computational neurodynamics. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 20(9):639-659.

[34]MaoYD, DongYJ, LuZZ, et al., 2025. Second-order locally active memristor based neuronal circuit. Chaos, Solitons & Fractals, 195:116279.

[35]MoonJ, LeebSB, 2016. Power electronic circuits for magnetic energy harvesters. IEEE Transactions on Power Electronics, 31(1):270-279.

[36]PershinYV, di VentraM, 2011. Memory effects in complex materials and nanoscale systems. Advances in Physics, 60(2):145-227.

[37]SchroedermeierA, LudoisDC, 2017. Integrated inductor and capacitor with co-located electric and magnetic fields. IEEE Transactions on Industry Applications, 53(1):‍380-390.

[38]ShaoY, WuFQ, WangQY, 2024. Synchronization and complex dynamics in locally active threshold memristive neurons with chemical synapses. Nonlinear Dynamics, 112(15):13483-13502.

[39]ShiF, CaoYH, BanerjeeS, et al., 2025. A neuronal circuit based on a second-order memristor. Nonlinear Dynamics, 113(10):12165-12183.

[40]ShiSY, LiangY, LiYQ, et al., 2024. A neuron circuit based on memristor and negative capacitor: dynamics analysis and hardware implementation. Chaos, Solitons & Fractals, 180:114534.

[41]SpornsO, 2010. Networks of the Brain. MIT Press, Cambridge, Massachusetts, USA.

[42]StrukovDB, SniderGS, StewartDR, et al., 2008. The missing memristor found. Nature, 453(7191):80-83.

[43]TakemboCN, MvogoA, Ekobena FoudaHP, et al., 2019. Effect of electromagnetic radiation on the dynamics of spatiotemporal patterns in memristor-based neuronal network. Nonlinear Dynamics, 95(2):1067-1078.

[44]WanJY, WuFQ, MaJ, et al., 2024. Dynamics and synchronization of neural models with memristive membranes under energy coupling. Chinese Physics B, 33(5):050504.

[45]WangBC, LvM, ZhangXF, et al., 2024. Dynamics in a light-sensitive neuron with two capacitive variables. Physica Scripta, 99(5):055225.

[46]WangCH, LuoZQ, 2022. A review of the optimal design of neural networks based on FPGA. Applied Sciences, 12(21):10771.

[47]WangCN, TangJ, MaJ, 2019. Minireview on signal exchange between nonlinear circuits and neurons via field coupling. The European Physical Journal Special Topics, 228(10):1907-1924.

[48]WangXJ, 2010. Neurophysiological and computational principles of cortical rhythms in cognition. Physiological Reviews, 90(3):1195-1268.

[49]WuFQ, WangRB, 2023. Synchronization in memristive HR neurons with hidden coexisting firing and lower energy under electrical and magnetic coupling. Communications in Nonlinear Science and Numerical Simulation, 126:107459.

[50]XuQ, FangYJ, FengCT, et al., 2024a. Firing activity in an N-type locally active memristor-based Hodgkin-Huxley circuit. Nonlinear Dynamics, 112(15):13451-13464.

[51]XuQ, DingXC, WangN, et al., 2024b. Spiking activity in a memcapacitive and memristive emulator-based bionic circuit. Chaos, Solitons & Fractals, 187:115339.

[52]YangFF, MaJ, RenGD, 2024a. A Josephson junction-coupled neuron with double capacitive membranes. Journal of Theoretical Biology, 578:111686.

[53]YangFF, MaJ, WuFQ, 2024b. Review on memristor application in neural circuit and network. Chaos, Solitons & Fractals, 187:115361.

[54]ZhaoJY, YuY, HanF, et al., 2024. Dynamic modeling and closed-loop modulation for absence seizures caused by abnormal glutamate uptake from astrocytes. Nonlinear Dynamics, 112(5):3903-3916.