Fig. 3

Intrinsic/synaptic dual homeostasis recovers original mean and variance after perturbation in a simulated firing rate model. Firing rate r is described by equation (15) with parameter values listed in Appendix 3. Input current is set to \(I{(t)} = \phi+ \sigma\xi{(t)}\), where \(\xi{(t)}\) is white noise with unit variance. In the top row of figures, \(\phi= 0.5\) and \(\sigma= 0.25\); in the bottom row of figures, \(\phi= 2.5\) and \(\sigma= 0.75\). (A) x and g trajectories plotted over time from two different initial conditions (orange and blue) as a fixed point is reached. (B) The same trajectories plotted in x/g phase space. (C) Mean firing rate \(\langle r \rangle\) (above) and firing rate variance \(\operatorname{var}(r)\) (below) are calculated as a function of homeostatic state \(({{x}}, g)\) and represented by color in x/g parameter space. The fixed point is marked in white. (D) Mean firing rate \(\langle r \rangle\) (above) and firing rate variance \(\operatorname{var}(r)\) (below) are plotted over time for both initial conditions. (E)-(H) When the mean and variance of the input current are increased, the system seeks out a new homeostatic fixed point. Note in G and H that, in spite of the new input statistics, a fixed point is reached with the same firing rate mean and variance