Analysis of global bifurcations in a market share attraction model

In this paper we demonstrate how the global dynamics of an economic model can be analyzed. In particular, as an application, we consider a market share attraction model widely used in the analysis of interbrand competition in marketing theory. We analyze the local and global dynamic properties of the resulting two-dimensional noninvertible dynamical system in discrete time. The main result of this paper is given by the study of some global bifurcations that change the structure of the attractors and their basins. These bifurcations are investigated by the use of critical curves, a powerful tool for the analysis of the global properties of noninvertible two-dimensional maps. (C) 2000 Elsevier Science B.V. All rights reserved. JEL classification. E32; M30.