State Transition Diagrams from the Nonlinear Equations

Computation of State Transition Diagrams from the Nonlinear Equations 

It is not a simple matter to determine whether the notion of state transition diagram introduced here provides a compact and useful method for representing flows of an arbitrary system of nonlinear kinetic equations. It is, however, possible to provide a list of some functional forms for i ,(x) that when substituted in Eq. (1) give differential equations of interest in chemical kinetics that can be readily classified. 

To determine the state transition diagram for Eqs. (1) and (16) it is convenient to define a Boolean variable 

We shall name each of the 2 volumes by a Boolean N-vector found from Eq. (18), which represents a vertex on the Boolean N-cube (the geometric dual of the concentration space). Consider the element / = 1. If mj = 0 in Eq. (16) then there will be a directed edge from (011 1) to (111 1) and if mi = 1, the orientation of this edge will be reversed. Similarly the edge joining (001 1) and (101 1) is directed from the first to the latter vertex if mi = 1, and if mi = 0 the orientation of this edge is reversed. The remainder of the edges are handled in similar fashion. 

Another functional form that generates kinetic equations classified using the same methods is  

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