Turing-like phenomenon on a discrete space-time

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Authors

POSPÍŠIL Zdeněk

Year of publication 2017
Type Appeared in Conference without Proceedings
MU Faculty or unit

Faculty of Science

Citation
Description We consider the coupled recurrences (difference equations) possessing an asymptotically stable equilibrium. A particular choice of the nonlinear functions appearing as their parameters enables one to interpret these equations as a model of a two-component chemical reaction, of two populations interaction, of two ideologies competition, and the like. Let us consider further a simple graph. A process of the reaction described by the previously mentioned recurrences in a node followed by diffusion of components (dispersion of populations) on the graph, i. e. a random move of a particle (individual) from a node to a neighbour one, can be described by certain discrete system. If the adjacency matrix of the graph is symmetric, then the system possesses a spatially homogeneous equilibrium. The aims of the contribution consist in demonstration that this equilibrium need not to be stable and in presenting conditions for the instability. That is, in describing a discrete analogy of the well known diffusion-driven or Turing instability. The research was motivated by attempts to model a diffusion dynamics of religious ideas and behavior forms.
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