Segregation process and phase transition in cyclic predator-prey models with even number of species

Abstract

We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of a square lattice. The evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly: if the sites are occupied by a predator-prey pair then the predator invades the prey's site; otherwise the species exchange their site with a probability $X$. For low $X$ values a self-organizing pattern is maintained by cyclic invasions. If $X$ exceeds a threshold value then two types of domains grow up that formed by the odd and even label species, respectively. Monte Carlo simulations indicate the blocking of this segregation process within a range of X for n=8.

5 pages, 5 figures, to be appear in Phys. Rev. E

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