Variational principles and the effect of a cutoff on population pattern size
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: email@example.com
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