Floquet theoretic approach to sensitivity analysis for periodic systems

The mathematical relationship between sensitivity analysis and Floquet theory is explored. The former technique has been used in recent years to study the parameter sensitivity of numerical models in chemical kinetics, scattering theory, and other problems in chemistry. In the present work, we derive analytical expressions for the sensitivity coefficients for models of oscillating chemical reactions. These reactions have been the subject of increased interest in recent years because of their relationship to fundamental biological problems, such as development, and because of their similarity to related phenomena in fields such as hydrodynamics, plasma physics, meteorology, geology, etc. The analytical form of the sensitivity coefficients derived here can be used to determine the explicit time dependence of the initial transient and any secular term. The method is applicable to unstable as well as stable oscillations and is illustrated by application to the Brusselator and to a three variable model due to Hassard, Kazarinoff, and Wan. It is shown that our results reduce to those previously derived by Edelson, Rabitz, and others in certain limits. The range of validity of these formerly derived expressions is thus elucidated.