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Energy evolution in function neuronal network under different coupling channels

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Abstract

Based on an auditory neuron model developed from the piezoelectric neuronal circuit, the Hamilton energy function is obtained by using the Helmholtz’s theorem, and this energy is contributed by the electric field and magnetic field described by capacitor and inductor, respectively. Three auditory neuronal circuits with different firing states are connected in a ring network by resistor, inductor, and capacitor. The coupling channels can be tamed under voltage, magnetic field, and electric field couplings simultaneously. These three types of coupling can modulate synchronization via continuous energy exchange and pumping, and the resistor channel consumes Joule heat, while the capacitor and inductor channels can pump and conserve field energy. The proportion of field energy maintained in each electrical component in the network is calculated separately to distinguish the dependence of firing state and synchronization mode on the energy. It is found that strong coupling increases the proportion of electric field energy in periodic neurons or the proportion of magnetic field energy in chaotic neurons. The total energy proportion of the three coupling channels continuously increases if all neurons in the network exhibit periodic firing. But the presence of neurons with chaotic firing causes the total energy proportion of the coupling channels to increase first and then decrease. In fact, more energy is injected into the inductor channel compared to resistor and capacitor, thus facilitating the synchronization of neurons connected by inductor.

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The datasets generated and/or analyzed in this work are available upon request from the corresponding author.

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Acknowledgements

The authors thanks Dr Feifei Yang for helpful verification and checking in the proof.

Funding

This work is supported from the National Natural Science Foundation of China (No.12062009).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Li Zhang & Wuyin Jin

  2. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, China

    Xinlei An

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  1. Li Zhang
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Zhang, L., Jin, W. & An, X. Energy evolution in function neuronal network under different coupling channels. Nonlinear Dyn 112, 8581–8602 (2024). https://doi.org/10.1007/s11071-024-09469-z

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