Dynamics оf globally coupled noisy FitzHugh-Nagumo neuron elements

We study the noisy FitzHugh-Nagumo model in the presence оf аn external sinusoidal driving force. We derive a Fokker-Planck equation for both the single element and for the globally coupled system. We introduce аn efficient way to numerically solve this Fokker-Planck equation and show that the external driving force leads to a classical resonance when its frequency matches the underlying systems frequency. This resonance is also investigated analytically by exploiting the different timescales in the problem. Agreement between the analytical results and numerical results is excellent and reveals the existence оf а stochastic bifurcation.