Kinetic equations their structure and properties

What are the simplest requirements if one wants to have a model for the time evolution of the concentration of chemical components or constituents in a reaction such as 

Using these more abstract notations the reaction in question takes the form 

Let us consider a small time interval (/, t + h) and let us make the simplest possible assumptions on the change of the components. These clearly are that. Vi(/ + h) - jci(0 depends on the quantities of the reacting components of the elementary reactions in which X(l) takes part. This dependence can be taken as linear, at least if the stoichiometric coeflScient of the component in question is one. If one takes the dependence on h to be linear too (at least up 

Furthermore, let us suppose that the effect of the single elementary reactions on the change do not interact, there is no cross-effect among them they simply sum up. 

How do we handle the problem when the stoichiometric coefficients are different from one The effect of the second elementary reaction on the change of X3(/) would be 

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