Analysis of noise effects in a map-based neuron model with Canard-type quasiperiodic oscillations

A problem of the mathematical modeling and analysis of the complex mixed-mode stochastic oscillations in neural activity is studied. For the description of noise-induced transitions between regimes of neuron dynamics, 2D map-based system near Neimark-Sacker bifurcation is used as a conceptual model. We focus on the parametric zone of Canard explosion where the attractors (closed invariant curves) are extremely sensitive to noise. Using direct numerical simulation and semi-analytical approach based on the stochastic sensitivity analysis, we study the noise-induced transformations from unimodal oscillations to bimodal spiking oscillations. The supersensitive invariant curve which marks the epicenter of the Canard explosion is found. It is shown that for this curve, the noise-induced splitting occurs for extremely small random forcing. Changes of the amplitude and frequency properties of the stochastic mixed-mode oscillations are studied. The phenomenon of noise-induced transitions from order to chaos is discussed.