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

Vicenc Méndez, W. Horsthemke, J. Casas-Vázquez, E. P. Zemskov

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1 Citation (Scopus)


The relation between pattern size and maximum population density is obtained for the stationary state of populations living in a refuge surrounded by ahostile environment. The population dynamics is described byreaction-diffusion equations whose kinetic terms display a cutoff. Thelatter takes into account the discreteness of the population when thepopulation density is small. We employ a variational principle for thenonlinear eigenvalue problem to obtain lower bounds for the pattern length. Numerical solutions display excellent agreement with our analytical results. © EDP Sciences/Societé Italiana di Fisica/Springer-Verlag 2007.
Original languageEnglish
Pages (from-to)189-197
JournalEuropean Physical Journal: Special Topics
Publication statusPublished - 1 Jul 2007


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