Global dynamics in a non-linear model of the equity ratio

A model for firms' financial conditions is proposed, which ultimately reduc es to a two-dimensional non-invertible map in the variables mean and varian ce of the equity ratio. The possible dynamics of the model and the global b ehaviour are investigated. We describe the mechanism of bifurcations leadin g to fractalization of the basins and/or fractalization of their boundaries ; showing how a locally stable attractor may be almost globally unstable. M ultistability is also investigated. Two, three or four co-existing attracto rs have been found and we describe the mechanism of bifurcations leading th eir basins to become chaotically intermingled, and thus to unpredictability of the asymptotic state in a wide region, The knowledge of such regimes, b esides those associated with simple dynamics, may be of help for the operat ors. While the use of the technical tools we propose to study the global dy namics and bifurcations may be of help for further investigations. (C) 2000 Elsevier Science Ltd. All rights reserved.