Non-linear mechanisms on graphs

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. 

The basic results in the analysis of non-linear mechanisms using graphs, were obtained by Clark [29], who developed a detailed formalism, and Ivanova [30, 31]. On the basis of Clark s approach, Ivanova formulated sufficiently general conditions for the uniqueness of steady states in terms of the graph theory. She suggested an algorithm that can be used to obtain (see Chap. 3, Sect. 5.4) 

Vol pert and Ivanova [32] suggested methods of searching for some 

Let us discriminate between the main problems in chemical kinetics solved using graph theory 

Problem (4) is typical of non-linear mechanisms. The number of studies in this field is essentially lower since the application of graph theory in nonlinear chemical kinetics is new. Our further description will relate to these principal problems. 

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