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Extinction and Chaotic Patterns in Map Lattices Under Hostile Conditions

Bulletin of Mathematical Biology volume 72, pages 432–443 (2010)Cite this article

Abstract

Population dynamics in spatially extended systems can be modeled by Coupled Map Lattices (CML). We employ such equations to study the behavior of populations confined to a finite patch surrounded by a completely hostile environment. By means of the Galerkin projection and the normal solution ansatz, we are able to find analytical expressions for the critical patch size and show the existence of chaotic patterns. The analytical solutions provided are shown to fit, under the appropriate approximations, the dynamics of a logistic map. This interesting result, together with our discussion, suggests the existence of a universal class of spatially extended systems directly linked to the well-known characteristics of the logistic map.

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Affiliations

  1. Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    Vicenç Méndez & Daniel Campos

  2. Departament de Física Fonamental, Facultat de Física, Universitat de Barcelona, Martí i Franquès, 08028, Barcelona, Spain

    Isaac Llopis

  3. Department of Chemistry, Southern Methodist University, Dallas, TX, 75275-0314, USA

    Werner Horsthemke

Authors
  1. Vicenç Méndez
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  2. Daniel Campos
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  3. Isaac Llopis
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  4. Werner Horsthemke
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Correspondence to Vicenç Méndez.

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Méndez, V., Campos, D., Llopis, I. et al. Extinction and Chaotic Patterns in Map Lattices Under Hostile Conditions. Bull. Math. Biol. 72, 432–443 (2010). https://doi.org/10.1007/s11538-009-9453-3

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  • DOI: https://doi.org/10.1007/s11538-009-9453-3

Keywords

  • Critical patch size
  • Extinction
  • Chaos
  • Coupled logistic map
  • Spatial pattern