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Variational principles and the effect of a cutoff on population pattern size

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Abstract.

The relation between pattern size and maximum population density is obtained for the stationary state of populations living in a refuge surrounded by a hostile environment. The population dynamics is described by reaction–diffusion equations whose kinetic terms display a cutoff. The latter takes into account the discreteness of the population when the population density is small. We employ a variational principle for the nonlinear eigenvalue problem to obtain lower bounds for the pattern length. Numerical solutions display excellent agreement with our analytical results.

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Authors and Affiliations

  1. Grup de Física Estadística, Universitat Autonoma de Barcelona, Facultat de Ciencies, edifici Cc, 08193-, Bellaterra Cerdanyola, Spain

    V. Méndez, J. Casas-Vázquez & E. P. Zemskov

  2. Department of Chemistry, Southern Methodist University, 75275-0314, Dallas, Texas, USA

    W. Horsthemke

Authors
  1. V. Méndez
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  2. W. Horsthemke
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  3. J. Casas-Vázquez
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  4. E. P. Zemskov
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Correspondence to V. Méndez.

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Méndez, V., Horsthemke, W., Casas-Vázquez, J. et al. Variational principles and the effect of a cutoff on population pattern size. Eur. Phys. J. Spec. Top. 146, 189–197 (2007). https://doi.org/10.1140/epjst/e2007-00179-6

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  • DOI: https://doi.org/10.1140/epjst/e2007-00179-6

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