Localized Mode-Locking Structure in the Stimulus Parameter Space for a Sinusoidally Forced FitzHugh–Nagumo Neuron

Neurons under periodic stimuli display various dynamical states including mode-locking tongues and firing onset, which has long been an interesting problem. The phase diagram in the parameter space and the bifurcations at the phase boundaries are investigated in a periodically driven FitzHugh–Nagumo neuron with the help of the bifurcation analysis and the continuation algorithm. The mode-locking structure is localized in the stimulus parameter space and enclosed by a curve, and the 1:1 firing state is dynamically equivalent to the nonfiring state. This localization is supposed to be originated from the polynomial form of the FitzHugh–Nagumo neural equation.