Noisy FitzHugh-Nagumo model: from single elements to globally coupled networks

We study the noisy FitzHugh-Nagumo model, representative of the dynamics of excitable neural elements, and derive a Fokker-Planck equation for both a single element and for a network of globally coupled elements. We introduce an efficient way to numerically solve this Fokker-Planck equation, especially for large noise levels. We show that, contrary to the single element, the network can undergo a Hopf bifurcation as the coupling strength is increased. Furthermore, we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency. This resonance is also investigated analytically by exploiting the different time scales in the problem.