  We study the dynamics of an intriguing crossover from a chaotic to a power
law state as a function of strain rate within the context of a recently
introduced model which reproduces the crossover. While the chaotic regime has a
small set of positive Lyapunov exponents, interestingly, the scaling regime has
a power law distribution of null exponents which also exhibits a power law. The
slow manifold analysis of the model shows that while a large proportion of
dislocations are pinned in the chaotic regime, most of them are pushed to the
threshold of unpinning in the scaling regime, thus providing insight into the
mechanism of crossover.
