Bifurcation analysis of a minimal neuron to ELF AC electric field

This paper investigates the bifurcation structure of a two-dimensional neuron model under external extremely low frequency (ELF) electric field. Neurons can exhibit rich dynamical states such as mode-locking and chaotic behaviors based on the two-dimensional minimal model. The bifurcation structure and the transitions between different neuronal firing patterns simulated by external electric field are explored by analyzing interspike intervals (ISIs). It is found that the frequency of the external electric field can act as a bifurcation parameter, whose small change can cause the transition of neuron behavior. There are myriads of Subcritical Hopf, inverse period-adding and period-doubling bifurcations forming the boundaries of the complex mode-locking structure.