Abstract:The continuous pumping and transmission of charged ions inside and outside the cell produces the electromagnetic induction effect which in turn affects the electrical activities and pattern switching of neurons and exhibits more abundant discharge characteristics. In this paper, based on the Chay neuron model under the influence of electromagnetic induction, a discontinuous control strategy with membrane voltage as the threshold is introduced, and the corresponding Filippov Chay neuron model is established to explore the neuron firing rhythm transitions and corresponding boundary motions under the influence of the threshold control strategy. Firstly, the boundary dynamics and sliding dynamics of the system are theoretically analyzed. Secondly, the diverse firing patterns of the system are explored using the single and two-parameter bifurcation diagrams. Thirdly, the equilibrium points of the system and their stability are investigated in detail by combining the Matcont simulation and stability theory. The sliding dynamics and the switching of various boundary motions generated under the influence of threshold are further explored by using the fast-slow dynamics analysis. Finally, the synchronization of coupled neurons under different thresholds is discussed by means of electrical synaptic coupling. Numerical simulation results show that the Filippov Chay system will produce sliding firing activities as well as corresponding traversing motion and grazing motion under the regulation of the threshold value. Besides, the number of firing cycles will also show different variation rules with the threshold value. For the cases of electrical synaptic coupling at different thresholds, the system will be stabilized in the firing state with a lower number of cycles after the system realizes the complete synchronization. The above results can contribute to a better understanding of the relevant control associated with neuronal sliding membrane as well as provide a certain help for further investigating the dynamical behavior of complex firing activities and information processing in biological nervous systems.