A theory for self-sustained balanced states in absence of strong external currents
Fig 8
Two distinct bifurcation mechanisms driving the instability of the homogeneous fixed point.
(A) Hopf bifurcation: two complex conjugate eigenvalues crosses the imaginary axis. (B) Zero-frequency bifurcation: One real eigenvalue crosses zero, leading to a stationary heterogeneous solution. In the insets in (A-B) are reported the firing activity of few excitatory (inhibitory) neurons above the corresponding transition displayed in orange (blue). (C) Distribution of the input currents for the excitatory population in a network simulation with heterogeneous fixed point (blue shaded histogram) and the Gaussian theoretical prediction (red line). Inset: Corresponding distribution of the synaptic efficacies. For panels A-C) we have used J0 = 1.0 and I0 = 0. (D) Theoretical prediction for the average input current (main) and the standard deviation (inset) as a function of the synaptic coupling J0. These correspond to the self-consistent solutions of Eqs (53) and (54). For all the panels in the figure we have considered .