The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 189–197 | Cite as

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

  • V. MéndezEmail author
  • W. Horsthemke
  • J. Casas-Vázquez
  • E. P. Zemskov


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.


Variational Principle European Physical Journal Special Topic Bifurcation Point Kinetic Term Travel Wave Solution 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • V. Méndez
    • 1
    Email author
  • W. Horsthemke
    • 2
  • J. Casas-Vázquez
    • 1
  • E. P. Zemskov
    • 1
  1. 1.Grup de Física Estadística, Universitat Autonoma de Barcelona, Facultat de CienciesBellaterra CerdanyolaSpain
  2. 2.Department of ChemistrySouthern Methodist UniversityDallasUSA

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