  The population model of Busenberg and Travis is a paradigmatic model in
ecology and tumour modelling due to its ability to capture interesting
phenomena like the segregation of populations. Its singular mathematical
structure enforces the consideration of regularized problems to deduce
properties as fundamental as the existence of solutions. In this article we
perform a weakly nonlinear stability analisys of a general class of regularized
problems to study the convergence of the instability modes in the limit of the
regularization parameter. We demonstrate with some specific examples that the
pattern formation observed in the regularized problems, with unbounded wave
numbers, is not present in the limit problem due to the amplitude decay of the
oscillations. We also check the results of the stability analysis with direct
finite element simulations of the problem.
