On irregular behavior of neuron spike trains

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.