Noise-induced Input Dependence in a Convective Unstable Dynamical System

Abstract

Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow dynamics, shows both analogue and digital changes, where the former is represented by oscillation frequency and the latter by different type of dynamics. The underlying universal mechanism for these changes is clarified by the spatial change of the co-moving Lyapunov exponent, with which the condition for the input dependence is formulated. The mechanism has a remarkable dependence on the noise strength, and works only within its medium range. Relevance of our mechanism to intra-cellular signal dynamics is discussed, by making our dynamics correspond to the auto-catalytic biochemical reaction for the chemical concentration, and the input to the external signal, and the noise to the concentration fluctuation of chemicals.