How fast elements can affect slow dynamics

A chain of coupled chaotic elements with different time scales is studied. In contrast with the adiabatic approximation, we find that correlations between elements are transferred from faster to 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, a bifurcation in the dynamics of the fastest element by changing its control parameter, and cascade propagation of the bifurcation. By studying coupled Rِssler equations, we demonstrate that fast elements can affect the dynamics of slow elements when these conditions are satisfied. The relevance of our results to biological memory is briefly discussed.