Estudio de la estabilidad y de las bifurcaciones de los equilibrios de un sistema dinámicoaplicación al mercado cervecero español

Zusammenfassung

This paper deals with the theory of codimension one bifurcations applied to a discrete-time economic dynamic model, that relates the current and potential market of a collective anyone. First, some necessary and suffi cient conditions are established for the stability of the only stationary state of the system, according to the values of the economic parameters of the model. This allow us to classify the equilibrium point in a parametric space. In this context, structural stability is a key point to study, that is, if the qualitative dynamic properties of the system persist when its structure is perturbed. The study of the structural stability is the fi rst step to follow in the analysis of the bifurcations lying in the system. The values of the parameters for which the system is not structurally stable are called bifurcation values. So secondly, changes in the number and/or the stability of stationay states are analyzed, focussing our attention on codimension one bifurcations (Flip, Fold and Neimark-Sacker bifurcations). Finally, a numerical example is presented where results are applied to the Spanish beer market. A time evolution analysis is made and we give economic sense to the obtained results.