Evdokia Slepukhina

We consider the Morris–Lecar neuron model with a parameter set corresponding to class 1 excitability. We study the effect of random disturbances on the model in the parametric zone where the only attractor of the deterministic system is a stable equilibrium. We show that under noise the stochastic generation of large amplitude oscillations occurs in the system. This phenomenon is confirmed by changes in distributions of random trajectories and interspike intervals. This effect is analyzed using the stochastic sensitivity function technique and the method of confidence domains. We suggest a criterion for the estimation of threshold values of noise intensity leading to the stochastic generation of oscillations.

We study the stochastic dynamics of FitzHugh–Nagumo model in the zone of limit cycles. For weak noise, random trajectories are concentrated in a small neighborhood of the initial deterministic unperturbed orbit of the limit cycle. As noise increases, in the zone of Canard cycles of the FitzHugh–Nagumo model, the bundle of random trajectories begins to split into two parts. This phenomenon is investigated using the density distribution of random trajectories. It is shown that the threshold noise intensity corresponding to the splitting bifurcation depends essentially on the degree of the stochastic sensitivity of the cycle. Using the stochastic sensitivity functions technique, a critical value corresponding to the supersensitive cycle is found and comparative parametric analysis of the effect of the stochastic cycle splitting in the vicinity of the critical value is carried out.