Excitatory-inhibitory homeostasis and bifurcation control in the Wilson-Cowan model of cortical dynamics
Fig 5
Behavior of the Wilson-Cowan model under multiple modes of homeostasis as a function of Iext and target firing rate ρ.
(A) Homeostatic values of GE (Left) and cEI (Right) (B) Homeostatic values of GE (Top left), cEI (Top right) and μE (Bottom) under homeostasis of GE, cEI and μE (C) Homeostatic values of GE (Top left), cEI (Top right) and μE (Bottom) under homeostasis of GE, cEI, μE and σE, with σE = KμE. In all plots, dashed lines represent the transition from stable fixed point to stable spiral, while solid lines show the Andronov-Hopf bifurcation between a stable spiral and a limit cycle. The parameters were estimated using a timestep of 0.1 ms. For each combination of modes, we include a diagram of the Wilson-Cowan model, indicating which model components are modulated by homeostatic plasticity. Blank areas relate to combinations of parameters for which the system has no solution (i.e. not possible to find a stable fixed point corresponding to ρ).