Segregation in a one-dimensional model of interacting species,
L. Frachebourg, P.L. Krapivsky, and E. Ben-Naim
We investigate segregation and spatial organization in a
one-dimensional system of N competing species forming a cyclic food
chain. For N<5, the system organizes into single-species domains, with
an algebraically growing typical size. For N=3 and N=4, the domains
are correlated and they organize into ``superdomains'' which are
characterized by an additional length scale. We present scaling
arguments as well as numerical simulations for the leading asymptotic
behavior of the density of interfaces separating neighboring domains.
We also discuss statistical properties of the system such as the
mutation distribution and present an exact solution for the case N=3.
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