Skip to main content
SpringerLink
Log in

Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model

  • Research Article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

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

    Article  Google Scholar 

  • Bao H, Liu WB, Ma J, Wu HG (2020) Memristor initial-offset boosting in memritive HR neuron model with hidden firing patterns. Int J Bifurc Chaos 30:2030029

    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 

  • Ding SK, Wang N, Bao H, Chen B, Wu HG, Xu Q (2023) Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: dynamics analysis and circuit implementation. Chaos Solit Fract 166:112899

    Article  Google Scholar 

  • Dou G, Zhao KX, Guo M, Mou J (2023) Memristor-based LSTM network for text classification. Fractals 2023:2340040

    Article  Google Scholar 

  • Fan WW, Chen XJ, Wang YT, Chen B, Wu HG, Xu Q (2023) Hidden firing patterns and memristor initial condition-offset boosting behavior in a memristive Hindmarsh-Rose neuron model. Front Phys 11:1160419

    Article  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Gao XY, Sun B, Cao YH, Banerjee S, Mou J (2023) A color image encryption algorithm based on hyperchaotic map and DNA mutation. Chin Phys B 32:030501

    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 J, Rose R (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 Phys 117:500–544

    CAS  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 

  • Izhikevich EM (2003) Simple model of spiking neurons. IEEE Trans Neural Netw 14:1569–1572

    Article  CAS  PubMed  Google Scholar 

  • Jia B, Gu HG, Li L, Zhao XY (2012) Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns. Cogn Neurodyn 6:89–106

    Article  PubMed  Google Scholar 

  • Jin 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 

  • Kafraj MS, Parastesh F, Jafri S (2020) Firing patterns of an improved Izhikevich neuron model under the effect of electromagnetic induction and noise. Chaos Solit Fract 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 

  • Kim SY, Lim W (2017) Dynamical responses to external stimuli for both cases of excitatory and inhibitory synchronization in a complex neuronal network. Cogn Neurodyn 11:395–413

    Article  PubMed  PubMed Central  Google Scholar 

  • Lai Q, Wan ZQ, Kuate PDK (2023) Generating grid multi-scroll attractors in memristive neural networks. IEEE Trans Circuits Syst I 70:1324–1336

    Article  Google Scholar 

  • Li CB, Jiang YC, Ma X (2021) On offset boosting in chaotic system. Chaos Theory Appl 3:47–54

    Article  CAS  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, Ma J (2016) Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205:375–381

    Article  Google Scholar 

  • Ma J (2023) Biophysical neurons, energy, and synapse controllability: a review. J Zhejiang Univ Sci A (Appl Phys Eng) 24:109–129

    Article  Google Scholar 

  • Ma J, Yang ZQ, Yang LJ, Tang J (2019) A physical view of computational neurodynamics. J Zhejiang Univ Sci A (Appl Phys Eng) 20:639–659

    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 

  • 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 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 

  • Rajagopal K, Moroz I, Karthikeyan A, Duraisamy P (2020) Wave propagation in a network of extended Morris-Lecar neurons with electromagnetic induction and its local kinetics. Nonlinear Dyn 100:3625–3644

    Article  Google Scholar 

  • Rao A, Plank P, Wild A, Maass W (2022) A long short-term memory for AI applications in spike-based neuromorphic hardware. Nat Mach Intell 4:467–479

    Article  Google Scholar 

  • Singh B, Jain C, Bansal A (2018) An improved adjustable step adaptive neuron-based control approach for the grid-supportive SPV system. IEEE Trans Ind Appl 54:563–570

    Article  Google Scholar 

  • Sun JW, Yang JL, Liu P, Wang YF (2022) Design of general flux-controlled and charge-controlled memristor emulators based on hyperbolic functions. IEEE Trans Comput-Aided Design Integr Circuits Syst 42:956–967

    Article  Google Scholar 

  • Sun JW, Wang YY, Liu P, Wen SP, Wang YF (2023) Memristor-based neural network circuit with multimode generalization and differentiation on Pavlov associative memory. IEEE Trans Cybernetics 53:3351–3362

    Article  Google Scholar 

  • Wang ZL, Shi XR (2020) Electric activities of time-delay memristive neuron disturbed by Gaussian whit noise. Cogn Neurodyn 14:115–124

    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 

  • Wang N, Xu D, Kuznetsov NV, Bao H, Chen M, Xu Q (2023) Experimental observation of hidden Chua’s attractor. Chaos Solit Fract 170:113427

    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 

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

    Article  Google Scholar 

  • Wouapi MK, Fotsin BH, Ngouonkadi EBM, Kemwoue FF, Njitacke ZT (2021) Complex bifurcation analysis and synchronization optical control for Hindmarsh-Rose neuron model under magnetic flow effect. Cogn Neurodyn 15:315–347

    Article  PubMed  Google Scholar 

  • Xu Y, Jia Y, Ge MY, Lu LL, Yang LJ, Zhan X (2018) Effects of ion channel blocks on electrical activity of stochastic Hodgkin–Huxley neural network under electromagnetic induction. Neurocomputing 283:196–204

    Article  Google Scholar 

  • Xu Y, Ma J, Zhan X, Yang LJ, Ja 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 Solit Fract 141:110353

    Article  Google Scholar 

  • Xu Q, Ju ZT, Ding SK, Feng CT, Chen M, Bao BC (2022) Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model. Cogn Neurodyn 16:1221–1231

    Article  PubMed  PubMed Central  Google Scholar 

  • Xu Q, Chen XJ, Chen B, Wu HG, Li Z, Bao H (2023a) Dynamical analysis of an improved FitzHugh-Nagumo neuron mode with multiplier-free implementation. Nonlinear Dyn 111:8737–8749

    Article  Google Scholar 

  • Xu Q, Wang YT, Iu HHC, Wang N, Bao H (2023b) Locally active memristor based neuromorphic circuit: firing pattern and hardware experiment. IEEE Trans Circuits Syst I 70:3130–3141

    Article  Google Scholar 

  • Xu Q, Liu T, Ding SK, Bao H, Li Z, Chen B (2023c) Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memritive electromagnetic induction. Cogn Neurodyn 17:755–766

    Article  PubMed  Google Scholar 

  • Xu Q, Wang YT, Chen B, Li Z, Wang N (2023d) Firing pattern in a memristive Hodgkin–Huxley circuit: numerical simulation and analog circuit validation. Chaos Solit Fract 172:113627

    Article  Google Scholar 

  • Yang YM, Ma J, Xu Y, Jia Y (2021) Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction. Cogn Neurodyn 15:265–277

    Article  PubMed  Google Scholar 

  • Yu F, Kang XX, A. Mokbel AM, Yao W, Cai S, (2023) Complex dynamics, hardware implementation and image encryption application of multiscroll memeristive Hopfield neural network with a novel local active memeristor. IEEE Trans Circuits Syst II 70:326–330

    Google Scholar 

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

    Article  Google Scholar 

  • Zhou XY, Xu Y, Wang GW, Jia Y (2020) Ionic channel blockage in stochastic Hodgkin-Huxley neuronal model driven by multiple oscillatory signals. Cogn Neurodyn 14:569–578

    Article  PubMed  PubMed Central  Google Scholar 

  • Zhou P, Eshraghian JK, Choi DU, Lu WD, Kang SM (2022) Gradient-based neuromorphic learning on dynamical RRAM arrays. IEEE J Emerg Selec Top Circuits Sys 12(4):888–897

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 12172066 and 52307002, the Natural Science Foundation of Jiangsu Province, China, under Grants BK20160282, the Project 333 of Jiangsu Province, the Scientific Research Foundation of Jiangsu Provincial Education Department, China, under Grant 23KJB120002, and the College Students’ Innovation and Entrepreneurship Training Program of Changzhou University.

Author information

Authors and Affiliations

  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159, People’s Republic of China

    Quan Xu, Kai Wang, Yufan Shan, Huagan Wu, Mo Chen & Ning Wang

Authors
  1. Quan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yufan Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Huagan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ning Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ning Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Q., Wang, K., Shan, Y. et al. Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model. Cogn Neurodyn 18, 645–657 (2024). https://doi.org/10.1007/s11571-023-10014-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-023-10014-8

Keywords

Search

Navigation