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We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation.

The response of a noisy FitzHugh-Nagumo (FHN) neuron-like model to weak periodic forcing is analyzed. The mean activation time is investigated as a function of noise intensity and of the parameters of the external signal. It is shown by numerical simulation that there exists a frequency range within which the phenomenon of resonant activation occurs; resonant activation is also observed in coupled FHN elements. The mean activation time with small noise intensity is compared with the theoretical results.