Spatial organization in cyclic Lotka-Volterra systems.

We study the evolution of a system of {ital N} interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with {ital N}{lt}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, {l_angle}l({ital t}){r_angle}{approximately}{ital t}{sup {alpha}}, where {alpha}=3/4 (1/2) and 1/3 for {ital N}=3 with sequential (parallel) dynamics and {ital N}=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, {l_angle}{ital L}({ital t}){r_angle}{approximately}{ital t}{sup {beta}}, with {beta}=1 and 2/3 for {ital N}=3 and 4, respectively. For {ital N}{ge}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 {ital N}=3. Some relevant extensions are also analyzed. {copyright} {ital 1996 The American Physical Society.}