Similarity of Sensitivity Functions of Reaction Kinetic Models

Abstract

Local sensitivity functions ∂Y i /∂ p k ; of many chemical kinetic models exhibit three types of similarity: (i) Local similarity: ratio λ i j = (∂Y i /∂p k )/(∂Y j /∂p k ) is the same for any parameter k. (ii) The scalingrelation: ratio λ i j is equal to (dY i /dz)/(dY j /dz). (iii) Global similarity: ratio (∂Y i /∂p k )/(∂Y i /∂p m ) is constant in a range of the independent variable z. It is shown that the existence of low-dimensional slow manifolds in chemical kinetic systems may cause local similarity. The scaling relation is present if the dynamics of the system is controlled by a one-dimensional slow manifold. The rank of the local sensitivity matrix is less than or equal to the dimension of the slow manifold. Global similarity emerges if local similarity is present and the sensitivity differential equations are pseudohomogeneous. Global similarity means that the effect of the simultaneous change of several parameters can be fully compensated for all variables, in a wide range of the independent variable by changing a single parameter. Therefore, the presence of global similarity has far-reaching practical consequences for the validation of complex reaction mechanisms, for parameter estimation in chemical kinetic systems, and in the explanation of the robustness of many self-regulating systems.