Comparison of Some Fractal Analysis Methods for Studying the Spontaneous Activity in Medullar Auditory Units

We recorded the spontaneous background impulse activity in the medullar and midbrain single auditory neurons of the paralyzed grass frog. This activity was considered by us as a chaotic point process. For the analyses of temporal changes of this process we used the approach based upon the recording of the Hurst index. This approach was juxtaposed with the methods based on the study of the dependence of Fano and Allan factors on the duration of the analyzed interval. A comparative analysis of the Fano, Allan and Hurst indices by Kendall's rank correlation method have been made. We observed a close correlation of the values of the Fano and Allan indices for the spontaneous activity of the same neuron. Correlation of the Fano and Hurst indices was not so pronounced and did not quite correspond to the properties of typical fractal point processes. It is possible to formulate assumptions about the possibility and efficiency of using Hurst index to analyze the sequence of pulsed discharges of a neuron. In most cells, chaotic changes in impulse density were observed, which is indicative of the trend behavior of neuron's firing. Anti-trend behavior was not observed.