Inhibitory Neurons Promote Robust Critical Firing Dynamics in Networks of Integrate-and-Fire Neurons

We study the firing dynamics of a discrete-state and discrete-time version of an integrate-and-fire neuronal network model with both excitatory and inhibitory neurons. When the integer-valued state of a neuron exceeds a threshold value, the neuron fires, sends out state-changing signals to its connected neurons, and returns to the resting state. In this model, a continuous phase transition from non-ceaseless firing to ceaseless firing is observed. At criticality, power-law distributions of avalanche size and duration with the previously derived exponents, −3/2 and −2, respectively, are observed. Using a mean-field approach, we show analytically how the critical point depends on model parameters. Our main result is that the combined presence of both inhibitory neurons and integrate-and-fire dynamics greatly enhances the robustness of critical power-law behavior (i.e., there is an increased range of parameters, including both sub- and supercritical values, for which several decades of power-law behavior occurs).