Superposition of modes in a caricature of a model for morphogenesis

In a model proposed for cell pattern formation by Nagorcka et al. (J. Theor. Biol. 1987) linear analysis revealed the possibility of an initially spatially uniform cell density going unstable to perturbations of two distinct spatial modes. Here we examine a simple one-dimensional caricature of their model which exhibits similar linear behaviour and present a nonlinear analysis which shows the possibility of superposition of modes subject to appropriate parameter values and initial conditions.