The structure of slow invariant manifolds and their bifurcational routes in chemical kinetic models

Abstract This article analyzes the global geometric properties of slow invariant manifolds in two-dimensional chemical kinetic models. By enforcing the concept of Lyapunov-type numbers, a classification of slow manifolds into global and generalized structures is obtained, and applied to explain the occurrence of different dynamic phenomena. Several related concepts such as stretching heterogeneity and α – ω inversion are introduced and commented by taking the Semenov system as a paradigmatic example. We show that the existence of a global slow manifold along with its properties are controlled by a transcritical bifurcation of the points at infinity, that can be readily identified by analyzing the Poincare projected (Pp) system. The information that can be obtained from the analysis of the Pp-system, and specifically the presence of saddle-points on the Poincare circle, are extremely helpful in the construction of a complete picture of the structure and properties of slow invariant manifolds even when the system exhibits non-hyperbolic equilibrium points or stable limit cycles.

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