• Rapid Communication

Pattern formation and coexistence domains for a nonlocal population dynamics

Jefferson A. R. da Cunha, André L. A. Penna, and Fernando A. Oliveira
Phys. Rev. E 83, 015201(R) – Published 13 January 2011

Abstract

In this Rapid Communication we propose a most general equation to study pattern formation for one-species populations and their limit domains in systems of length L. To accomplish this, we include nonlocality in the growth and competition terms, where the integral kernels now depend on characteristic length parameters α and β. Therefore, we derived a parameter space (α,β) where it is possible to analyze a coexistence curve α*=α*(β) that delimits domains for the existence (or absence) of pattern formation in population dynamics systems. We show that this curve is analogous to the coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations.

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  • Received 17 September 2010

DOI:https://doi.org/10.1103/PhysRevE.83.015201

© 2011 American Physical Society

Authors & Affiliations

Jefferson A. R. da Cunha1,2, André L. A. Penna2,3, and Fernando A. Oliveira2,4,*

  • 1Instituto de Física, Universidade Federal de Goiás, CP 131 CEP 74001-970, Goiânia, Brasil
  • 2International Center for Condensed Matter Physics, CP 04455, 70919-970 Brasilia DF, Brazil
  • 3Faculdade do Gama-FGA, Universidade de Brasília, Brasília, Brasil
  • 4Instituto de Física, Universidade de Brasília, Brasília, Brasil

  • *fao@fis.unb.br

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Vol. 83, Iss. 1 — January 2011

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