Quantifying Strength of Chaos in the Population Firing Rate of Neurons

Abstract

In this study, I considered quantifying the strength of chaos in the population firing rate of a pulse-coupled neural network. In particular, I considered the dynamics where the population firing rate is chaotic and the firing of each neuron is stochastic. I calculated a time histogram of firings to show the variation in the population firing rate over time. To smooth this histogram, I used Bayesian adaptive regression splines and a gaussian filter. The nonlinear prediction method, based on reconstruction, was applied to a sequence of interpeak intervals in the smoothed time histogram of firings. I propose the use of the sum of nonlinearity as a quantifier of the strength of chaos. When applying this method to the firings of a pulse-coupled neural network, the sum of nonlinearity was seen to satisfy three properties for quantifying the strength of chaos. First, it can be calculated from spiking data alone. Second, it takes large values when applied to firings that are confirmed, theoretically or numerically, to be chaotic. Third, it reflects the strength of chaos of the original dynamics.