Formation, dynamics and properties of stable moving patterns in a simple model of neural tissue
Andrey Yu. Verisokin, Kursk State University, Russia
Darya V. Verveyko, Kursk State University, Russia
Dmitry E. Postnov, Saratov State University, Russia
Abstract
Recent theoretical studies mostly show the instable character of wave fronts in continuous excitable media. Nevertheless, the time and space discrete media, in particular cellular automata, can provide the propagating self-sustained space-stable structures. In mathematical models of neural tissues the medium can be considered as a discrete one as it is formed by single cells connected via diffusion in a continuous small-volume medium. We base on the extended FitzHugh–Nagumo model and account the changes of intercellular volume. In such a model medium single stable small-size wave patterns are observed. The following key features of these patterns should be highlighted: (i) the steady character of the patterns, so small deviations do not change their form; (ii) with an increase in the size of the pattern perpendicular to the direction of motion, the size of the pattern increases; iii) a small rotation of the pattern leads to the return of the pattern to its original shape, a large rotation turns the pattern into a spiral wave; iv) such patterns exist at a certain diffusion interval.
Speaker
Andrey Yu. Verisokin
Kursk State University
Russia
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