On the Transition from Local Regular to Global Irregular Fluctuations.

We present a general framework for understanding the transition from local regular to global irregular (chaotic) bahaviour of nonlinear dynamical models in discrete time. The fundamental mechanism is the unfolding of quadratic tangencies between the stable and the unstable manifolds of periodic saddle points. To illustrate the relevance of the presented methods for analyzing globally a class of dynamic economic models, we apply them to the infinite horizon model of Woodford [34], amended by Grandmont, Pintus and de Vilder [13] to account for capital-labor substitution, so as to explain the appearance of irregular fluctuations, through homoclinic bifurcations, when parameter values are far away from local bifurcation points.