JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (5): 1-11.doi: 10.6040/j.issn.1671-9352.0.2020.712

   

Firing and synchronization of a neocortical neuron under electromagnetic induction

QI Hui-min1, ZHANG Li2, AN Xin-lei1*, QIAO Shuai1, XIAO Ran1   

  1. 1.School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China;
    2.Department of Basic Science, Lanzhou Institute of Technology, Lanzhou 730050, Gansu, China
  • Published:2021-05-13

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Abstract: A four-dimensional neuron model of a class of neocortical neurons is established by introducing the flux variable to modulate the membrane potential of the electromagnetic induced current. Based on single parameter bifurcation diagram, the double parameter bifurcation diagram and the corresponding maximum Lyapunov exponent diagram analysis of the discharge characteristics of the model in detail and bifurcation model, the numerical results show that the model in the appropriate external stimuli and under the action of electromagnetic induction intensity will produce complex bifurcation behaviors, namely periodic bifurcation and period-doubling and inverse period-doubling bifurcation, etc. Interestingly, the model has a “comb-shaped” chaotic structure in a two-parameter plane, which means that the model has a period-added bifurcation model with chaos. Meanwhile, based on Lyapunov stability theory, it is proved that the model can achieve complete synchronization under appropriate flux coupling strength, but will destroy the synchronization behavior under strong coupling condition.

Key words: electromagnetic coupling, neocortical neurons, bifurcation analysis, maximum Lyapunov exponent, complete synchronization

CLC Number: 

  • O441.3
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