Coexisting firing analysis in a FitzHugh–Nagumo neuron system

Dynamics analysis of neuronal models has been attracting more attention, which may offer a valuable perspective for studying neurons. To address this issue, the improved FitzHugh–Nagumo neuron model with applied driving current will be explored through the implicit mapping method to better explore the complex motions. The evolution of periodic motion to chaos of such a neuron is analyzed and the bifurcation types are decided from the eigenvalue plots. The bifurcation diagrams of period-1 to period-4 and period-3 to period-6 are obtained through the period doubling bifurcation and saddle bifurcation. With the use of the membrane potential's phase diagram and time history, neuronal spiking events can be precisely exhibited. The coexistence of stable and unstable firing patterns of FHN neuron model are explored through the semi-analytical method, which cannot be obtained by conventional methods. Additionally, the circuit implement of system is developed using FPGA, and the oscilloscope provides a complete set of unstable and stable phase diagrams, which validate the results of the semi-analytical method. The advancements in brain medicine and artificial intelligence may also benefit from this research.