A model of the expression of gap genes during the early development of Drosophila embryo has been studied. The parameter values for the model have been obtained by fitting the solutions to experimental patterns under an additional assumption of the asymptotic stability of solutions at large times. The patterns at the beginning of gastrulation in these solutions are very close to the actual attractor in the model. It is shown that these solutions have a better stability, or robustness, to perturbations of concentrations and parameter values in the model.