avalanches in a stochastic model of spiking neurons雪崩飙升的随机模型神经元.pdf

Avalanches in a Stochastic Model of Spiking Neurons 1. 2 1,3 2 . Marc Benayoun , Jack D. Cowan , Wim van Drongelen , Edward Wallace * 1 Department of Pediatrics, University of Chicago, Chicago, Illinois, United States of America, 2 Department of Mathematics, University of Chicago, Chicago, Illinois, United States of America, 3 Computation Institute, University of Chicago, Chicago, Illinois, United States of America Abstract Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( w105 neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly t