On the transition from local regular to global irregular fluctuations

✍ Scribed by Patrick Pintus; Duncan Sands; Robin de Vilder

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 390 KB
• Volume: 24
• Category: Article
• ISSN: 0165-1889
• DOI: 10.1016/s0165-1889(98)00071-2

✦ Synopsis

We present a general framework for understanding the transition from local regular to global irregular (chaotic) behaviour 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 analysing globally a class of dynamic economic models, we apply them to the in"nite horizon model of Woodford ( 1988), (J. Economic Theory, 40, 128}137), amended by Grandmont et al. ( 1998), (J. Economic Theory, 80) to account for capital-labour substitution, so as to explain the appearance of irregular #uctuations, through homoclinic bifurcations, when parameter values are &far' away from local bifurcation points.