  A chain of coupled chaotic elements with different time scales is studied. In
contrast with the adiabatic approximation, we find correlations between faster
and slower elements when the differences in the time scales of the elements lie
within a certain range. For such correlations to occur, three features are
essential: strong correlations among the elements allowing for both
synchronization and desynchronization, bifurcation in the dynamics of the
fastest element by the change of its control parameter, and the cascade
propagation of the bifurcation. The relevance of our results to biological
memory is briefly discussed.
