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Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model

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Abstract

Neurons can exhibit abundant electrical activities due to physical effects of various electrophysiology environments. The electromagnetic induction flows can be triggered by changes in neuron membrane potential, which can be equivalent to a memristor applying on membrane potential. To imitate the electromagnetic induction effects, we propose a three-variable memristor-based Wilson neuron model. Using several kinetic analysis methods, the memristor parameter- and initial condition-related electrical activities are explored intensively. It is revealed that the memristive Wilson neuron model can display rich electrical activities, including the asymmetric coexisting electrical activities and antimonotonicity phenomenon. Finally, using off-the-shelf discrete components, an analog circuit on a hardware level is implemented to verify the numerically simulated coexisting electrical activities. Studying these rich electrical activities in neurons can build the groundwork to widen the neuron-based engineering applications.

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References

  • An XL, Qiao S (2021) The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction. Chaos Solitons Fractals 143:110587

    Article  Google Scholar 

  • Bao BC, Bao H, Wang N, Chen M, Xu Q (2017) Hidden extreme multistability in memristive hyperchaotic system. Chaos Solitons Fractals 94:102–111

    Article  Google Scholar 

  • Bao BC, Hu AH, Xu Q, Bao H, Wu HG, Chen M (2018a) AC induced coexisting asymmetric bursters in the improved Hindmarsh-Rose model. Nonlinear Dyn 92:1695–1706

    Article  Google Scholar 

  • Bao H, Liu WB, Hu AH (2018b) Coexisting multiple firing patterns in two adjacent neurons coupled by memristive electromagnetic induction. Nonlinear Dyn 95:43–56

    Article  Google Scholar 

  • Bao H, Zhu D, Liu WB, Xu Q, Chen M, Bao BC (2020a) Memristor synapse-based Morris-Lecar model: Bifurcation analysis and FPGA-based validations for periodic and chaotic bursting/spiking firings. Int J Bifurc Chaos 30:2050045

    Article  Google Scholar 

  • Bao H, Hu AH, Liu WB, Bao BC (2020b) Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans Neural Netw Learn Sys 31:502–511

    Article  Google Scholar 

  • Bao BC, Zhu YX, Ma J, Bao H, Wu HG, Chen M (2021) Memristive neuron model with an adapting synapse and its hardware experiments. Sci China Tech Sci 64:1107–1117

    Article  Google Scholar 

  • Carpenter CJ (1999) Electromagnetic induction in terms of the Maxwell force instead of magnetic flux. IEE Proc Sci Meas Technol 146:182–193

    Article  Google Scholar 

  • Chay TR (1985) Chaos in a three-variable model of an excitable cell. Physica D 16:233–242

    Article  Google Scholar 

  • Chua LO (2015) Everything you wish to know about memristors but are afraid to ask. Radioengineering 24:319–367

    Article  Google Scholar 

  • Dawson SP, Grebogi C, Yorke JA, Kan I, Koçak H (1992) Antimonotonicity: inevitable reversals of period-doubling cascades. Phys Lett A 162:249–254

    Article  Google Scholar 

  • FitzHugh R (1961) Impulses and physiological states in theoretical model of nerve membrane. Biophys J 1:445–466

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ge MY, Jia Y, Xu Y, Yang LJ (2018) Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn 91:515–523

    Article  Google Scholar 

  • Gu HG, Pan BB, Li YY (2015) The dependence of synchronization transition processes of coupled neurons with coexisting spiking and bursting on the control parameter, initial value, and attraction domain. Nonlinear Dyn 82:1191–1210

    Article  Google Scholar 

  • Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164

    Article  CAS  PubMed  Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Imani MA, Ahmadi A, Malekshahi MR, Haghiri S (2019) Digital multiplierless realization of coupled Wilson neuron model. IEEE Trans Biomed Circuits Syst 12:1431–1439

    Article  Google Scholar 

  • ** WY, Wang A, Ma J, Lin Q (2019) Effects of electromagnetic induction and noise on the regulation of sleep wake cycle. Sci China Technol Sci 62:2113–2119

    Article  Google Scholar 

  • Jiang YN, Huang P, Zhu DB, Han RZ, Liu LF, Liu XY, Kang JF (2018) Design and hardware implementation of neuromorphic systems with RRAM synapses and threshold-controlled neurons for pattern recognition. IEEE Trans Circuits Syst I Reg Papers 65:2726–2738

    Article  Google Scholar 

  • Kafraj MS, Parastesh F, Jafari S (2020) Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise. Chaos Solitons Fractals 137:109782

    Article  Google Scholar 

  • Kengne J, Negou AN, Tchiotsop D (2017) Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based Jerk circuit. Nonlinear Dyn 88:2589–2608

    Article  Google Scholar 

  • Li CB, Thio WJ, Sprott JC, Zhang RX, Lu TA (2017) Linear synchronization and circuit implementation of chaotic system with complete amplitude control. Chin Phys B 26:120501

    Article  Google Scholar 

  • Liu Y, Ma J, Xu Y, Jia Y (2019) Electrical mode transition of hybrid neuronal model induced by external stimulus and electromagnetic induction. Int J Bifurc Chaos 29:1950156

    Article  Google Scholar 

  • Lv M, Wang CN, Ren GD, Ma J, Song XL (2016) Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn 85:1479–1490

    Article  Google Scholar 

  • Ma J, Tang J (2017) A review for dynamics in neuron and neuronal network. Nonlinear Dyn 89:1569–1578

    Article  Google Scholar 

  • Manimehan I, Philominathan P (2012) Composite dynamical behaviors in a simple series–parallel LC circuit. Chaos Solitons Fractals 45:1501–1509

    Article  Google Scholar 

  • Mondal A, Upadhyay RK, Ma J, Yadav BK, Sharma SK, Mondal A (2019) Bifurcation analysis and diverse firing activities of a modified excitable neuron model. Cogn Neurodyn 13:393–407

    Article  PubMed  PubMed Central  Google Scholar 

  • Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193–213

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Nouri M, Hayati M, Serrano-Gotarredona T, Abbott D (2019) A digital neuromorphic realization of the 2D Wilson neuron model. IEEE Trans Circuits Syst II Express Briefs 66:136–140

    Google Scholar 

  • Parastesh F, Rajagopal K, Karthikeyan A, Alsaedi A, Hayat T, Pham VT (2018) Complex dynamics of a neuron model with discontinuous magnetic induction and exposed to external radiation. Cogn Neurodyn 12:607–614

    Article  PubMed  PubMed Central  Google Scholar 

  • Pinto RD, Varona P, Volkovskii AR, Szücs A, Abarbanel HD, Rabinovich MI (2000) Synchronous behavior of two coupled electronic neurons. Phys Rev E 62:2644–2656

    Article  CAS  Google Scholar 

  • Qi Y, Watts AL, Kim JW, Robinson PA (2013) Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos. Biol Cybern 107:15–24

    Article  CAS  PubMed  Google Scholar 

  • Rostami Z, Jafari S (2018) Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction. Cogn Neurodyn 12:235–254

    Article  PubMed  PubMed Central  Google Scholar 

  • Steyn-Ross DA, Steyn-Ross ML, Wilson MT, Sleigh JW (2006) White-noise susceptibility and critical slowing in neurons near spiking threshold. Phys Rev E 74:051920

    Article  CAS  Google Scholar 

  • Steyn-Ross ML, Steyn-Ross DA (2016) From individual spiking neurons to population behavior: systematic elimination of short-wavelength spatial modes. Phys Rev E 93:022402

    Article  PubMed  Google Scholar 

  • Wang Y, Ma J, Xu Y, Wu FQ, Zhou P (2017) The electrical activities of neurons subject to electromagnetic induction and Gaussian white noise. Int J Bifurc Chaos 27:1750030

    Article  Google Scholar 

  • Wilson HR (1999) Simplified dynamics of human and mammalian neocortical neurons. J Theor Biol 200:375–388

    Article  CAS  PubMed  Google Scholar 

  • Wu FQ, Wang CN, Xu Y, Jun M (2016) Model of electrical activity in cardiac tissue under electromagnetic induction. Sci Rep 6: Article no. 28

  • Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16(3):285–317

    Article  Google Scholar 

  • Xu Q, Lin Y, Bao BC, Chen M (2016) Multiple attractors in a non-ideal active voltage-controlled memristor based Chua’s circuit. Chaos Solitons Fractals 83:186–200

    Article  Google Scholar 

  • Xu Y, Ma J, Zhan X, Yang LJ, Jia Y (2019) Temperature effect on memristive ion channels. Cogn Neurodyn 13:601–611

    Article  PubMed  PubMed Central  Google Scholar 

  • Xu Q, Tan X, Zhu D, Bao H, Hu YH, Bao BC (2020) Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit. Chaos Solitons Fractals 141:110353

    Article  Google Scholar 

  • Yang YM, Ma J, Xu Y, Jia Y (2020) Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction. Cogn Neurodyn 15:265–277

    Article  PubMed  PubMed Central  Google Scholar 

  • Ye WJ, Mai WD, Hu GW (2018) Effects of the electromagnetic radiation on cognitive performance: a model study. Nonlinear Dyn 93:2473–2485

    Article  Google Scholar 

  • Zhao X, Kim JW, Robinson PA, Rennie CJ (2013) Low dimensional model of bursting neurons. J Comput Neurosci 36:81–95

    Article  PubMed  Google Scholar 

  • Zhou L, Wang CH, Zhang X, Yao W (2018) Various attractor, coexisting attractors and antimonotonicity in a simple fourth order memristive Twin-T oscollator. Int J Bifurc Chaos 28:1850050

    Article  Google Scholar 

Download references

Acknowledgements

We are very grateful for the valuable comments from the anonymous referees. This work was supported by the grants from the National Natural Science Foundation of China under Grant Nos. 12172066, 61801054, and 51777016, the Natural Science Foundation of Jiangsu Province, China under Grant Nos. BK20160282 and BK20191451, and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China under Grant No. KYCX20_2547.

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  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, People’s Republic of China

    Quan Xu, Zhutao Ju, Shoukui Ding, Chengtao Feng, Mo Chen & Bocheng Bao

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  1. Quan Xu
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  2. Zhutao Ju
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  3. Shoukui Ding
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  4. Chengtao Feng
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  6. Bocheng Bao
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Correspondence to Bocheng Bao.

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Xu, Q., Ju, Z., Ding, S. et al. Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model. Cogn Neurodyn 16, 1221–1231 (2022). https://doi.org/10.1007/s11571-021-09764-0

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