Fig. 3
From: NREM sleep in the rodent neocortex and hippocampus reflects excitable dynamics
Recurrence, adaptation, and drive determine dynamical regime and duration statistics. a Effective I/O curves for populations with increasing levels of recurrent excitation, w. Solid lines indicate stable fixed points, dotted lines indicate unstable fixed points, and circles indicate the upper/lower bounds of a limit cycle. Yellow indicates bistable regime (2 stable fixed points), blue indicates oscillatory regime (0 stable fixed points with a stable limit cycle). See also Supplementary Figs. 3 and 4. b Regions in the w-b parameter plane for distinct I/O properties, indicated by insets. Blue shading indicates parameter values for a oscillatory-centered I/O curve, yellow shading indicates a bistable-centered I/O curve. Boundary curves correspond to parameters where bifurcations vs I coalesce, see Supplementary Note 3. wPF: pitchfork bifurcation separating 5-fixed point and 3-fixed point (2 stable) regimes. wχ: degenerate pair of saddle node bifurcations, separating bistable-centered and oscillatory-centered I/O curves. w0: degenerate Hopf bifurcation separating oscillatory-centered and monotonic stable I/O curves. c Simulated duration distributions on the oscillatory-centered I/O curve. (Top) Simulated time course (r vs t) and dwell time distributions (bottom) for low (I = 2.6), intermediate (I = 3), and high (I = 3.4) levels of drive. (Bottom) UP/DOWN state duration distributions as a function of drive to the system. Note logarithmic axis of duration. Color reflects observed proportion of UP/DOWN states with a given duration. d Same as c, for the bistable-centered I/O curve. e Duration statistics as a signature of UP/DOWN regime. (Left) Ratio of simulation time in UP and DOWN state. (Right) Mean and CV of simulated dwell times for UP and DOWN states in the I-W parameter space with fixed b (triangle in 3B)
