Convective instability with time scale translation of the transmitted fluctuation

Convective instability in an open flow system with distributed time scales from upstream to downstream is studied. By exploiting the convective instability, the upstream fluctuation with fast time scale is not only amplified along the flow but is also slowed down along the flow to the downstream. Through the instability, statistical property of the downstream shows sensitive dependence on the dynamics of the fast element in the upstream, and the fast dynamics is translated into slower dynamics. This convective instability and sensitive dependence on the boundary are analyzed, by noting the time scale multiplication of fluctuation with repetition of bifurcation through the transmission. Relevance of this process to biochemical reaction and memory is discussed.