Fig 5. Network-generated oscillations.

Oscillatory population spike rate and mean adaptation current of 50,000 excitatory coupled aEIF neurons and each of the derived models (for constant external input moments) generated by the interplay of recurrent excitation/adaptation current (A) and by delayed recurrent inhibition (B). In addition, the limit cycle of the LN_exp model is shown in terms of the (quantity) steady-state spike rate r_∞ as a function of effective input moments μ_eff, ${\sigma }_{\text{eff}}^2$ (A, top) and for the spec₂ model in dependence of the total input moments (μ_tot, ${\sigma }_{\text{tot}}^2$ (A, bottom). The phase of the cycle is visualized by grayscale color code (increasing phase from black to white). The values for the input, adaptation and coupling parameters were μ_ext = 1.5 mV/ms, ${\sigma }_{\text{ext}}=2\text{mV}/\sqrt{\text{ms}}$, a = 3 nS, b = 30 pA (A, top), μ_ext = 1.275 mV/ms, ${\sigma }_{\text{ext}}=1.5\text{mV}/\sqrt{\text{ms}}$, a = 3 nS, b = 60 pA (A, bottom), K = 1000, J = 0.03 mV, τ_d = 3 ms (A, both). In B adaptation was removed (a = b = 0) and delays were identical d_ij = d; input and coupling parameter values were μ_ext = 1.5 mV/ms, ${\sigma }_{\text{ext}}=1.5\text{mV}/\sqrt{\text{ms}}$, K = 1000, J = −0.0357 mV, d = 10 ms (top) and μ_ext = 3 mV/ms, ${\sigma }_{\text{ext}}=2\text{mV}/\sqrt{\text{ms}}$, K = 1000, J = −0.087 mV, d = 5 ms (bottom).