Bifurcation analysis of a modified FitzHugh-Nagumo neuron with electric field

Abstract

This paper is devoted to investigating the analytical solutions of the modified FitzHugh-Nagumo (FHN) neuron model with external electric fields through by the discrete mapping method, which can provide a new perspective to the study of complex motions of the neuron. The bifurcation trees of period-1 to period-8 motions and period-3 to period-12 motions of FHN neuron are presented through the implicit discrete mapping method, and the stable and unstable orbits, which cannot study through the traditional numerical method, are calculated. The bifurcations and stability of the periodic orbits are developed via eigenvalues. The spiking firing of neurons can be observed through the discrete nodes in phase portraits and time histories of membrane potential. Moreover, the antimonotonicity of improved FHN model is reported with varying the controlled parameters. The two-parameter diagrams are employed to intuitively explain the generation and evolution of periodic motions. Moreover, the modified FHN system is implemented via hardware circuit, the experiments of which validate the semi-analytical method. The investigation results are useful for the development of artificial intelligence and medicine.