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Energy dependence on modes of electric activities of neuron driven by multi-channel signals

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Abstract

Neuron can receive electric signals or forcing currents from more than one channel, and these forcing currents could show some diversity. Based on the Hindmarsh–Rose neuron model, mixed forcing currents, which are composed of low-frequency, high-frequency and constant signals, are imposed on the neuron, and multiple modes of electric activities could be observed alternately (in turn) from the neuron. Based on the Helmholtz theorem, the Hamilton energy is calculated to discern the energy dependence on the mode selection of the electric activities of neuron. It is found that the response of electrical activities much depends on the amplitude than the frequency when mixed signals are imposed on the neuron synchronously; however, the rhythm of electrical activities could be adjusted by the frequency of the periodical signals in the mixed signal. It is confirmed that the energy is much dependent on the mode of electrical activities instead of the external forcing currents directly, and a smaller energy occurs under bursting states. The delayed response of Hamilton energy to external forcing currents confirms that neuron contributes to energy coding. These results could be helpful for further investigation on energy problems in neuronal network associated with model transition for collective behaviors.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China under Grant Nos. 11365014 and 11372122.

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Authors and Affiliations

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

    Ya Wang, Chunni Wang & Guodong Ren

  2. School of Physics, China University of Mining and Technology, Xuzhou, 221116, China

    Jun Tang

  3. College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Wuyin Jin

  4. NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Chunni Wang

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  1. Ya Wang
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Correspondence to Chunni Wang.

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Wang, Y., Wang, C., Ren, G. et al. Energy dependence on modes of electric activities of neuron driven by multi-channel signals. Nonlinear Dyn 89, 1967–1987 (2017). https://doi.org/10.1007/s11071-017-3564-4

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  • DOI: https://doi.org/10.1007/s11071-017-3564-4

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