  Recent studies on the Portevin - Le Chatelier effect report an intriguing
crossover phenomenon from a low dimensional chaotic to an infinite dimensional
scale invariant power law regime in experiments on CuAl single crystals and
AlMg polycrystals, as a function of strain rate. We devise a fully dynamical
model which reproduces these results. At low and medium strain rates, the model
is chaotic with the structure of the attractor resembling the reconstructed
experimental attractor. At high strain rates, power law statistics for the
magnitudes and durations of the stress drops emerge as in experiments and
concomitantly, the largest Lyapunov exponent is zero.
