Fig. 5: Stabilizing effect of delay variability.
From: Myelin-induced gain control in nonlinear neural networks
a–c Gaussian delay distributions (left) determine the shape of the mean field power spectral density S(ω) (right). The Gaussian mean and variance are independent from each other. Here, the mean delay is kept constant and given by m = kθ/c, while the variance is increased from s2 = 0.01 to 0.5 (lines with increased shading). To compute the power spectral density, we assumed a stimulus S(t) with noise variance D = 0.05 and zero bias i.e., I = 0. The dashed line corresponds to the Lorentzian power spectral density associated with \(\bar{J}=0\). Increasing the conduction velocities shifts the mean delay towards smaller values. Conduction velocities are given by c = 5.0 m/s (blue lines, (a)); c = 2.5 m/s (black lines, (b)); c = 1.0 m/s (red lines, (c)). d–f Eigenvalues associated with the characteristic polynomial (cf. Eq. (26) in the Methods section) whenever conduction velocity c is fixed and the delay variance s2 is varied. Increasing the delay dispersion s2 shifts the oscillatory eigenvalues away from the imaginary axis and stabilizes the dynamics. Different conduction velocities are given by c = 5.0 m/s (blue shading, (d)), c = 2.5 m/s (black shading, (e)) and c = 1.0 m/s (red shading, (f)). Other parameters are \(\bar{J}=0.9\), ρ = 1, k = 2, θ = 4 mm, I = 0, and the activation function is nonlinear with parameters β = 2, h = 0.5.
