Abstract
We introduce a simple model of a growing system with competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical time the first isolated cluster occurs. In the one-dimensional system the volume of the new phase, i.e., the number of the isolated individuals, increases with time as . For a large number of possible communities, the critical density of filled space is equal to , where is the system size. A similar transition is observed for Erdős-Rényi random graphs and Barabási-Albert scale-free networks. Analytical results are in agreement with numerical simulations.
- Received 16 September 2008
DOI:https://doi.org/10.1103/PhysRevE.80.036103
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