We addressed the formation of dislocation patterns by using a reaction
-diffusion model (proposed some years ago) where well-known dislocatio
n interaction mechanisms are represented by linear and non-linear term
s. The non-linear analysis developed shows that it is possible to obta
in a rich dynamical behaviour with spatial and/or temporal patterns, w
hich one could be tempted to associate to those observed experimentall
y (e.g. persistent slip bands, rod-like structures or cell structures)
. However, the transformation of the reaction-diffusion model into its
Ginzburg-Landau equation leads to unexpected results showing the limi
tation of the model.