Complex reaction bipartite graph

Investigations with the graphs of non-linear mechanisms had been stimulated by an actual problem of chemical kinetics to examine a complex dynamic behaviour. This problem was formulated as follows for what mechanisms or, for a given mechanism, in what region of the parameters can a multiplicity of steady-states and self-oscillations of the reaction rates be observed Neither of the above formalisms (of both enzyme kinetics and the steady-state reaction theory) could answer this question. Hence it was necessary to construct a mainly new formalism using bipartite graphs. It was this formalism that was elaborated in the 1970s. 

Bipartite graphs for presenting complex mechanisms of chemical reactions have been proposed by Vol pert (1972) and Hudyaev and Vol pert (1985). These graphs contain nodes of two types type X nodes corresponding to components X, (/ = 1, 2,. ..,N) and type R nodes ascribed to... 

The structure of graphs of complex reactions is very important for the analysis of chemical dynamics. The absence of oriented cycles indicates relatively simple dynamic behavior. Clarke (1980) and Ivanova (Ivanova, 1979 Ivanova and Tamopolskii, 1979) used bipartite graphs for... 

Fig. 4.21 Bipartite graph for the reaction mechanism in Fig. 4.20. (From O.N. Temkin, Kinetic models of multi-route reactions in homogeneous catalysis with metal complexes (a review), Kinet. Catal. 53 (2012) 313-343. Copyright 2012 Springer).

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