Flows in Kinetic Systems

Flow Box Analysis in Chemical Kinetics 3.1. Classification of Flows in Kinetic Systems 

Assume that there is a chemical kinetic system described by Eqs. (1) and (2), We decompose the concentration space into 2 volumes, which are arranged in space so that they are homeomorphic (topologically equivalent) to the 2 orthants in the neighborhood of the origin in an N-dimensional coordinate space. There are boundaries between the contiguous 

This construction takes continuous flows in N-dimensions and represents them in a finite way so that combinatorial methods can be employed to obtain a classification of the dynamics. (This should be compared with the methods of 

The structural equivalence classes for N=2. The number in parentheses under each structure gives the number of systems falling in each equivalence class. 

One of the structural equivalence classes, shown in Fig. 4, has been of particular interest in the study of oscillations in chemical networks with three interacting chemicals. It has appeared in an analysis of the Field-Noyes equations for the Belousov-Zhabotinsky reaction, and in an analysis of 

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