This paper discusses ergodic properties and circular statistical characteristics in neuronal spike trains. Ergodicity means that the average taken over a long time period and over smaller population should equal the average in less time and larger population. The objectives are to show simple examples of design and validation of a neuronal model, where the ergodicity assumption helps find correspondence between variables and parameters. The methods used are analytical and numerical computations, numerical models of phenomenological spiking neurons and neuronal circuits. Results obtained using these methods are the following. They are: a formula to calculate vector strength of neural spike timing dependent on the spike train parameters, description of parameters of spike train variability and model of output spiking density based on assumption of the computation realized by sound localization neural circuit. Theoretical results are illustrated by references to experimental data. Examples of neurons where spike trains have and do not have the ergodic property are then discussed.

Department of Mathematics and Statistics Faculty of Science Masaryk University Kotlarska 2 61137 Brno Czech Republic

Institute of Pathological Physiology 1st Medical Faculty Charles University U Nemocnice 5 12853 Prague 2 Czech Republic

Max Planck Institute for the Physics of Complex Systems Noethnitzer Strasse 38 01187 Dresden Germany Czech Technical University Prague Zikova 1903 4 16636 Prague 6 Czech Republic

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