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A review for dynamics in neuron and neuronal network

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Abstract

The biological Hodgkin–Huxley model and its simplified versions have confirmed its effectiveness for recognizing and understanding the electrical activities in neurons, and bifurcation analysis is often used to detect the mode transition in neuronal activities. Within the collective behaviors of neurons, neuronal network with different topology is designed to study the synchronization behavior and spatial pattern formation. In this review, the authors give careful comments for the presented neuron models and present some open problems in this field, nonlinear analysis could be effective to further discuss these problems and some results could be helpful to give possible guidance in the field of neurodynamics.

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Acknowledgements

This work is partially supported by the National Nature Science Foundation of China under the Grant No. 11672122.

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Authors and Affiliations

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

    Jun Ma

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

    Jun Ma

  3. NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jun Ma

  4. Department of Physics, China University of Mining and Technology, Xuzhou, 221116, China

    Jun Tang

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Ma, J., Tang, J. A review for dynamics in neuron and neuronal network. Nonlinear Dyn 89, 1569–1578 (2017). https://doi.org/10.1007/s11071-017-3565-3

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