Traffic jams induce dynamical phase transition in spatial rock–paper–scissors game.

Spatial and temporal behaviors of the rock–paper–scissors (RPS) game is key to understanding not only biodiversity but also a variety of cyclic systems. It has been demonstrated that, in the stochastic cellular automaton of RPS game, three species cannot survive on one-dimensional (1-d) lattice; only a single species survives. Previous studies have shown that three species are able to coexist if the migration of species is considered. However, their definitions of migration are the swapping of two species or the random walk of species, which rarely occurs in nature. Here, we investigate the effect of migration by using the 1-d lattice traffic model in which species can move rightward if the site ahead is empty. Computer simulations reveal that three species can survive at the same time within the wide range of parameter values. At low densities, all species can coexist. In contrast, the extinction of two species occurs if the density exceeds the critical limit of the jamming transition. This dynamical phase transition between the coexistence and single (non-coexistence) phase clearly separates due to the self-organized pattern: condensation and rarefaction in the stripe-pattern of three species. [ABSTRACT FROM AUTHOR]