Descriptive Reaction Kinetics

By a complex chemical reaction we mean a set of reaction steps , where are chemical species (molecules, radicals, ions, etc.), the non-negative integers and are the stoichiometric coefficients or molecularities, and the formal linear combinations and are the reactant and product complexes, respectively. The vectors and , that is, and , corresponding to the reaction complexes, are the complex vectors, the reactant complex vector, and the product complex vector, respectively. If a complex vector is the null vector, then the corresponding reaction complex is the empty complex, denoted by 0. The reaction step vector expressing the change caused by the reaction step is the difference of complex vectors: . The matrix with as its column is the stoichiometric matrix.

One may identify the formal reaction mechanism with the four ordered elements: , where is the set of formal chemical species, is the set of reaction steps, with , and are the matrices of type with column vectors and , respectively.

By the continuous time and continuous state place deterministic model (CCD) of the formal reaction mechanism we mean the following differential equation:
, where the function is sometimes called the kinetic, and the most common type of is when it is mass-action kinetic, that is, there are positive real constants, such that for any , . ( is the concentration of the chemical component at time .) One may call the differential equation above the induced kinetic differential equation of the formal reaction mechanism .

P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models, Manchester: Manchester University Press, 1989.