Spatial organization in cyclic Lotka-Volterra systems

We study the evolution of a system of N interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with $N<5$ species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing average size, 〈(t)〉~t^α, where α=3/4(1/2) and 1/3 for $N=3$ with sequential (parallel) dynamics and $N=4$, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, 〈L(t)〉~t^β, with β=1 and 2/3 for N=3 and 4, respectively. For $N>~5$, the system quickly reaches a frozen state with noninteracting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as well as an exact solution for $N=3$. Some relevant extensions are also analyzed.