Effects of heterogeneity and noise on homeostatic stability of a network.

<p>A) The stability as a function of heterogeneity in the neurons’ homeostatic time-constants. The time-constants <i>τ</i>₁, <i>τ</i>₂, <i>τ</i>₃ for each neuron were drawn from gamma-distributions with means 10, 50 and 100ms, respectively, and a CV given by the x-axis. The curve represents the mean maximal recurrence allowed to ensure a stable system. It decreases with heterogeneity. Error bars represent the standard deviation over 1000 trials. Simulation of 10 neurons, connected with a random, fixed weight matrix. B) Noise does not ameliorate instability. The fluctuations in the population firing rate, due to both noise and oscillations, are plotted as a function of the network recurrence. Without noise, fluctuations are only present when the recurrence exceeds the critical value (dashed curve). With noise, the fluctuations are already present in the stable regime and increase close to the transition point (solid curve). The homeostasis in the system amplifies noise compared to the non-homeostatic system (grey line). Homeostatic time-constants were 10, 50 and 100ms.