Identification of observed dynamic centres for analysis of experimental data

Abstract

The parameter space is divided by hypersurfaces called bifurcation sets into regions having different dynamic features. These sets intersect or coalesce at singular points. A physical centre is either a transversal intersection next to which three or more regions with different dynamic features exist or a tangential intersection next to which at least two regions with different dynamic features exist. The observable centres of systems described by two variables having widely separated time scales are classified according to their nature and number of observable regions in their vicinity. The assumption of widely separated time scales allows derivation of analytical expressions defining the bifurcation sets and centres. The classification and identification of the centres should be helpful in the organization of experimental data, in a search of new dynamic features, and in the development of a mathematical model of the observations. The latter point is demonstrated by identifying a centre which predicts experimental observations by Gray et al. (1984, 8 th Int. Symp. of Chem. Reaction Engng, Edinburgh, pp. 101–108) and constructing a model which predicts it.