Turing-like phenomenon on a discrete space-time
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| Year of publication | 2017 |
| Type | Appeared in Conference without Proceedings |
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| 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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