To start the reaction, the participation of product B is required. Thus, before the reaction, one must mix a small amount of B into the system; otherwise, if starting from 100% A without B’s participation, a first B product will never be generated, which means that the reaction will never occur.

Actually, in a real reaction system, what often occurs is the parallel existence of two reactive paths:

i.e., A can convert to B by the first pathway (**Fn**), just before the time where the second autocatalytical pathway (**Bna**), under the “catalysis” of B , becomes to be significant.

This kind of reaction can be called a combined Kamal-Sourour auto-catalysis reaction. Under the assumption that the activation energies of the two paths are the same, we got the partial case of Eq12, the function Cnm:

If we look further into the function, we’ll see that the reaction rate is presented as the sum of two items, namely Fn and Bna. Additionally, there’s a weight factor (auto-catalysis factor) K_{cat} to represent the contribution of Bna, or it can also be said that the frequency factors of the two paths are different.

Simplified versions of Cnm include C1 (both exponents n and m = 1, i.e., the combination of F1 and B1) and Cn (m=0, namely the reaction order of A is n while B plays the role as first-order). Cn is more commonly used.

If assuming the activation energies of the two paths are different, the general Kamal-Sourour reaction type is used:

This reactaion type is the sum of reactions Fn and Bna with a different values of Ea and a certain weight factor (or different frequency factor).

Reactions C1, Cn, Cmn are the simplified case of the general Kamal-Sourour reaction with two competitive pathways. Being the combination of an n-th order and an auto-catalysis reaction, a combined auto-catalysis reaction will exhibit accelerating performance in between that of a pure n-th order reaction and a pure auto-catalysis reaction; i.e., there will be a certain induction period, and after that, the reaction’s acceleration will be more significant than n-th order, but not as dramatic as the pure auto-catalysis Prout-Tompkins reaction. Of course, the actual accelerating behavior depends on the combination weight of the two paths.