Study of power-law activity distributions in a two-dimensional model system

Activities observed in a neural system, especially superficial cortical layers, often show cascades of bursts, called neuronal avalanches, and the distribution of them obeys a power law. Some hypotheses have been suggested for the principle underlying the phenomenon. One of the suggestions is that such a power-law activity distribution emerges as a specific form of the stationary solution of the Markov process, rather than the criticality, and some special characteristics in the spiking dynamics are the important ones causing the phenomenon. Various properties of activity distributions in all-to-all connection structures have been well explained based on the theory, but there is a lack of studies on the activities in a more cortical-like structure. Motivated by the point, the properties of activities in a two-dimensional structure are investigated in this paper. The firing statistics observed in the cortex may not be properly implemented if an incorrect reduction model is used. In this paper, presented is one of the minimal models to reproduce the experimental observations in simulations.