On Irregular Behavior of Neuron Spike Trains

Abstract

The computational analysis of neuron spike trains shows that the changes in monotony of interspike interval values can be described by a special type of real numbers. As a result of such an arithmetical approach, we establish the presence of chaos in neuron spike trains and arrive at the conclusion that in stationary conditions, brain activity is found asymptotically close to a multidimensional Cantor space with zero Lebesgue measure, which can be understood as the brain activity attractor. The self-affinity, power law dependence, and computational complexity of neuron spike trains are also briefly examined and discussed.

Fractals in the nervous system: conceptual implications for theoretical neuroscience

“…Re-working some of Wise's data, West and Deering ( 1994 ) identified fractal (hyperbolic) spike interval distributions. Taking an entirely different approach to conceptualizing irregular behavior in neuron spike trains led Shahverdian and Apkarian ( 1999 ) to discuss self-affinity, power-Law dependence, and computational complexity of spike trains in terms of a multidimensional Cantor space with zero Lebesgue measure as attractor.…”

A theorem on higher-order differences of two-state Markov chains

“…In this paper an application of the suggested in [1]- [7] difference analysis to studying the two-state Markov chains is presented. The difference analysis is a method for studying irregular and random time series, based on consideration of higher-order absolute differences taken from the series' progressive terms.…”