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A feasible neuron for estimating the magnetic field effect

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Abstract

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

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Acknowledgements

This project is partially supported by National Natural Science Foundation of China under the Grant Nos. 11672122 and 12072139.

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Authors and Affiliations

  1. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Yin Zhang, Ying Xu, Zhao Yao & Jun Ma

  2. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, China

    Ying Xu

  3. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 430065, China

    Jun Ma

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Zhang, Y., Xu, Y., Yao, Z. et al. A feasible neuron for estimating the magnetic field effect. Nonlinear Dyn 102, 1849–1867 (2020). https://doi.org/10.1007/s11071-020-05991-y

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