https://doi.org/10.1140/epjst/e2007-00179-6
Variational principles and the effect of a cutoff on population pattern size
1
Grup de Física Estadística, Universitat Autonoma de Barcelona, Facultat de Ciencies, edifici Cc, 08193-, Bellaterra Cerdanyola, Spain
2
Department of Chemistry, Southern Methodist University, 75275-0314, Dallas, Texas, USA
Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
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.
© EDP Sciences, Springer-Verlag, 2007
