Bifurcations and aggregation in large scale systems

Abstract

This paper deals with the following problem: assume that a qualitative analysis (behaviour modes, bifurcation points, type of atractors .•• ) of a nonlinear dynamical system has been carried out and that afterwards this dynamical system is transformed into a large scale system through a disaggregating process of some (or all) of its variables. The problem at stake is to analyze whether the disagaregation gives rise to new behaviour modes, as a consequence of the appearance of new bifurcations in the disaggregated dynamical system. That leads us to study whether the original system and the disaggregated one are "equivalents" or whether the second one is richer in behaviours than the first one.The paper develops general results for standard disaggregation forms. Furthermore, practical applications of the proposed methodology to urban dynamics models is included .