title: Inhibitory neurons promote robust critical firing dynamics in networks of integrate-and-fire neurons.
abstract: 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).
authors.affiliation: Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.|Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Zhixin
authors.initials: Z
authors.lastname: Lu
authors.affiliation: Department of Physics, University of Maryland, College Park, Maryland 20742, USA.|Intel Corporation, Hillboro, Oregon 97124, USA.
authors.forename: Shane
authors.initials: S
authors.lastname: Squires
authors.affiliation: Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.|Department of Physics, University of Maryland, College Park, Maryland 20742, USA.|Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
authors.affiliation: Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA.|Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA.|Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Michelle
authors.initials: M
authors.lastname: Girvan
mesh_terms: D000818:Animals; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology*