Figure 8.

Extracting microscopic features from mesoscopic identification. (A) Nullclines $\stackrel{.}{\nu }=0$ of the identified field component G from LIF network simulations at different levels of recurrent synaptic excitation J_rec, spanning the red dashed line in Figure 7A (see colored labels, J_rec sampled at steps of 1 mV). Adaptation level fixed at g_c = 20 mV/s. Dotted colored curves: fitted nullcline approximations at drift-dominated regime as in Figure 4A. Black dashed line: nullcline $ċ=0$. Inset: estimated absolute refractory period τ₀ versus J_rec; dashed red line, expected value. (B) Correlation between J_rec and the real part of the eigenvalues λ of the Eq. 2Jacobian, using the identified G(c,ν) around the equilibrium point ∼(1,4 Hz). Red dashed line: linear regression (p < 10⁻³, t-test). Green vertical line: Hopf bifurcation predicted by the linear fit. Insets: examples of ν(t) dynamics for Re(λ) < 0 (top left) and Re(λ) > 0 (bottom right) close to the equilibrium point. (C) Oscillation periods of ν(t) given by inverse Im(λ). Oscillations are damped only at the left of the Hopf bifurcation (green vertical line).