Figure 7. Stochastic resonance in a noisy and delayed neural oscillator.

(A) We investigated the dynamics of a conceptual delayed feedback model in the presence of periodic forcing (i.e. stimulation) as a proxy for the thalamo-cortical circuit subjected to additive noise. The mean activity $u$ experiences delayed feedback with delay $T$, additive noise and periodic forcing. (B) Amplitude of entrained solution both above and below the Hopf bifurcation threshold. Below the bifurcation (black line), the linear gain $\left|R_{th}\right|$ remains high because noise intensity is small. Solutions have a high amplitude only near the intrinsic critical frequency. Above the bifurcation (orange line), the linear gain $\left|R_{th}\right|$ becomes smaller under the effect of noise. As a consequence, the amplitude of all non-resonant solutions increases, while the amplitude of resonant solution decreases. (C) Peak power at ${\omega }_{stim}$ in the rest (black) and task (orange) states as stimulation frequency varies in the vicinity of ${\omega }_o$. Although resulting from a more complex model, the effect remains qualitatively similar to the simplified case in (B).