The application of dynamical systems qualitative analysis techniques to the study of models of socio-economical systems showing abrupt changes in its qualitative behaviour is proposed. The approach is based on the multiple time-scale properties of a class of non-linear perturbed systems. The change of qualitative behaviour produced in the system can be explained through the singularities of a properly defined surface. The proposed technique is applied to a system dynamics model which describes the collapse of the Maya civilization. The relatively complex model constitutes an excellent illustration of the possibilities of the proposed method. In addition, the example studied in this paper shows the essential role of the non-linearities in modelling the qualitative change, thus pointing out the inherent limitations of the linear models (traditionally used in econometrics) in this sort of problem.
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