Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits
Fig 5
Stability analysis of the homogeneous, asynchronous state of the spatially-extended spiking circuit.
(A) Mean firing rate of the excitatory population in the simulation of our local cortical circuits (dots) and the rate of spatially uniform activity from the analysis (solid line) with the optimal correction factor. The dashed line shows the critical point ζ = ζc. (B) Eigenvalues with the largest real parts of the network’s dynamics in response to spatially periodic perturbations (spatial Fourier mode k = (1, 1)), with different I-E ratios ζ and the optimal correction factor. The eigenvalues in this parameter regime are real, with positive values emerging as the I-E ratio ζ decreases below the critical point ζc (dashed line), indicating a Turing bifurcation. The dominant spatial eigenmode has wave vector k = (1, 1), indicating that a single pattern is formed, consistent with that observed in the full spiking circuit.