A multi-frequency whole-brain neural mass model with homeostatic feedback inhibition
Fig 2
Bifurcation analysis of the model with and without plasticity.
A) Bifurcation diagram, main oscillatory frequency, and two sample activity traces at the indicated p input values, for the original Jansen-Rit model without plasticity and consisting only of α population (10 Hz). Below the traces, a power spectral density (PSD) plot is shown. In the left panel, red thick lines and black lines represent stable and unstable fixed points, respectively. Colored lines represent maxima and minima of stable (green) and unstable (blue) periodic orbits. The colors are maintained in the center panel to show the frequency (in Hz) of the associated oscillations. Dots denote the bifurcations encountered: purple = saddle-node bifurcations and saddle-node of limit cycles; black = Hopf bifurcation. Simulations include a noise factor added to the p parameter. B) Same as in (A), with the addition of the homeostatic plasticity mechanism and a target for pyramidal target firing rate ρ = 2.5 Hz. Blue dots denote a Torus or Neimar-Sacker bifurcation. The shaded rectangle in the left panel denotes the range of p that is plotted in (A). C) Same as in (B), with the target ρ = 3.5 Hz. Red dot denotes a branching or pitchfork bifurcation.