Dynamics analysis and Hamilton energy control of a class of Filippov neuron model

Abstract

Electromagnetic induction plays a key role in regulating the electrical activity, excitability, and bistable structure of neurons. In this paper, a discontinuous control strategy with membrane potential as the threshold is introduced to the HR neuron model under the influence of electromagnetic field (EMFN model), and then we establish a Filipov EMFN neuron model to realize the regulation effect of electromagnetic field on the neuron system. Specific work of this paper reads as follows: first, the existence and stability of equilibrium points of two subsystems are analyzed by using MatCont software; second, the bistable region and its internal mechanism are discussed in detail by two-parameter bifurcation analysis; third, the mechanism of bistability and a series of complex sliding mode dynamics including sliding segment and sliding bifurcations are further revealed with the help of the fast–slow variable dissection method; finally, based on Hamilton energy, the regulation of threshold on chaotic discharge in the Filippov EMFN neuron model is explored. The numerical simulation results show that the EMFN neuron model can produce the corresponding sliding limit cycle and sliding bursting behaviors under the influence of the threshold control strategy, meanwhile, the chaotic behavior of the new system can be controlled effectively within a certain range. The results provide ideas for controlling the effects of electromagnetic fields on the biological neuronal system and exploring the regulation mechanism of neurological diseases.