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.}

• Publication year

  1996

• Venue

  Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

• Publication date

  1996-06-11

• Fields of study

  Biology, Physics, Mathematics, Environmental Science, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.54.6186arXiv cond-mat/9606069PMID 9965838
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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