Amplification of noise in a cascade chemical reaction

Networks of chemical reactions have been given much attention recently. However, dynamical aspects of such networks remain to be elucidated. In this paper, we study a cascade chemical reaction, consisting of a series of downstream-coupled Brusselators. Along the cascade of reaction, small fluctuations naturally existing in the concentration of chemical species are amplified. Such amplification of small noise leads to the formation of chemical oscillations in the downstream chemical species. The amplification rate of small noise in the concentration along the cascade is studied and the method to calculate the amplification rate analytically is developed. It is also shown that the nonlinear evolution of the chemical oscillation in the downstream reaction strongly depends on the frequency of the initial inlet chemical concentration.