Spatial organization in cyclic Lotka-Volterra systems

Details Spatial organization in cyclic Lotka-Volterra systems Spatial organization in cyclic Lotka-Volterra systems

1996-06-11

arxiv.org/abs/cond-mat/9606069v1

Phys. Rev. E 54, 6186 (1996)

Physics

Condensed Matter

18 pages, 10 figures, revtex, also available from http://arnold.uchicago.edu/~ebn/

Scientific paper

10.1103/PhysRevE.54.6186

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 size, $\ell(t)\sim t^\alpha$, where $\alpha=3/4$ (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, ${\cal L}(t)\sim t^\beta$, with $\beta=1$ and 2/3 for N=3 and 4, respectively. For $N\geq 5$, the system quickly reaches a frozen state with non interacting 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 possible extensions of the system are analyzed.

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