8. Similarity of Sensitivity Functions

If a model is strongly autocatalytic and very different timescales are present, both of which are characteristic features of many reaction kinetic models, then the calculated local sensitivity functions are usually similar to each other. An implication of this is that in many cases, by changing a number of input parameters simultaneously according to certain ratios, almost identical simulation results can be obtained for output variables of kinetic models, over quite wide ranges of concentrations or reaction conditions. The similarity relations can be sorted into categories of local similarity, scaling relationships and global similarity. Such similarity relations have been found in models of combustion systems (explosions and flames) and molecular biological models. The theory of the origin of all these similarity relations is discussed in this chapter. The similarity of sensitivity functions is related to several important topics, such as discrimination between models, uniqueness of a model and robustness of biological systems.