The Edge of Stability: Response Times and Delta Oscillations in Balanced Networks
Fig 2
Response of the balanced network to changes in NMDA/AMPA ratio.
A: Network schematic showing the structure of the rate model used in simulations. Triangular synapses are excitatory and circular synapses are inhibitory. For LIF networks E and I represent populations of 3,200 and 800 neurons respectively with probability of connection between neurons of p = 0.2. B: Simulation of the rate based network for three values of Δq. At the smallest value, delta oscillations appear (blue line). This value is in the orange range in D, for even smaller values the system is unstable. All rate based networks use k = 1.2, w = 30. C: Same for the LIF network but with k = 0.65 and w = 5.0. D: Rise time in seconds as a function of Δq for the rate model. Red squares indicate instabilities, the orange segment represents the values of Δq which generate delta oscillations, and the dashed black line is at the value of Δq where the rise time is 100 ms. E: Frequency response of the linear system. Delta oscillations start for small negative Δq (blue) and gamma oscillations (green) appear when Δq approaches the right instability in D.