Consensus in Small and Large Audiences
We consider the dynamics of a population in which individuals select a color from a finite set of colors. Each individual in the population has a “neighborhood” and the choices made by the neighbors influence the selection process of that individual. We are interested in the dynamics of the evolution of such a system to the monochromatic state of unison. We consider how the mean time to unison varies with the sizes of the population and the neighborhood, the geometry of the neighborhoods and the initial number of colors. Some analytical results are presented for the case where the size of the neighborhood is the entire population. Results of computer experiments for a variety of scenarios are presented and discussed.
KeywordsMonte Carlo Simulation Periodic Boundary Condition Absorption Time Diffusion Approximation Neighbor Site
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