Figure 1

(a) Network mean firing rate ${\nu }_0$ as a function of the level of heterogeneity $w$ for three bias values. (b) Stability line separating the asynchronous and synchronous regimes. In both panels, numerical simulations of Eqs. (1, 2, 3) (points) confirm our mean-field predictions (lines). Insets in (b) show a typical time evolution of the mean firing rate for the corresponding behavior. Coupling strength $J$ is 10 mV (a) or 20 mV (b). Here and below, unless specified otherwise, we have $N=1500$, ${\tau }_m=20\mathrm{ms}$, $R=0.1\mathrm{G}\Omega$, $V_r=10\mathrm{mV}$, ${\tau }_r=5\mathrm{ms}$, $D=2\mathrm{ms}$, $\overline{\theta }=20\mathrm{mV}$, and $\sigma =3\mathrm{mV}$.Reuse & Permissions

Figure 2

(a) Time varying firing rate (lower red line) of an heterogeneous ($w=4\mathrm{mV}$) neural population to a slowly modulated signal (blue upper line) in the asynchronous regime, corresponding to a rate coding scheme. (b) Input/output correlation as a function of $w$. (c) Response of an heterogeneous ($w=2.5\mathrm{mV}$) neural population, close to the stability line, to a train of deltalike pulses (blue triangles), corresponding to a temporal coding scheme. (d) PPV is optimized for a given value of the heterogeneity. The time window used to identify a TP event was $\Delta t=10\mathrm{ms}$. Inset: as suggested by our analysis, $w^{*}$ closely follows the mean-field stability line (blue line). For panels (a) and (b): $\mu =14\mathrm{mV}$, $J=10\mathrm{mV}$, $A_s=0.5\mathrm{mV}$, and $f_s=2\mathrm{Hz}$. For panels (c) and (d): $\mu =14\mathrm{mV}$ (varying in inset), $J=20\mathrm{mV}$, $A_p=1\mathrm{mV}$, and $f_p=3\mathrm{Hz}$.Reuse & Permissions

Figure 3

(a) Input/output correlation as a function of $w$ for different modulation frequencies $f_s$ in the rate coding scheme. (b) Dependence of the optimal heterogeneity level $w^{*}$ on $f_s$. Labels indicate the type of brain wave corresponding to this region. For both panels (a) and (b), $A_s=0.5\mathrm{mV}$, $J=10\mathrm{mV}$, and $\mu =14\mathrm{mV}$. (c) PPV as a function of $w$ for different values of $f_p$, in the temporal coding scheme. (d) Dependence of the peak value ${\mathrm{PPV}}^{*}$ on $f_p$. For both panels (c) and (d), $A_p=1\mathrm{mV}$, $J=20\mathrm{mV}$, and $\mu =13\mathrm{mV}$. (e) Mean firing rate for a network of 800 excitatory and 200 inhibitory neurons. Connectivity is sparse (400 afferent connections per neuron), coupling strength is 30 mV for excitatory synapses and $-60\mathrm{mV}$ for inhibitory ones. Panel (f) shows the I/O correlation for such a realistic network with an input sine wave as in Fig. 2a, except for $\mu =15\mathrm{mV}$.Reuse & Permissions