Chaotic Solutions in the Lucas model

JOHNSON A. R.;VENTURI, BEATRICE

2009-01-01

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Abstract

CHAOTIC SOLUTIONS IN THE LUCAS MODEL In this paper we show that the investigation of limit set regular or chaotic is of central importance to economists who care about the long run impact of policies and institutions (see inter al. Lorenz H.W.,1989, Benhabib J. 1992, Medio A. 1992, Jarsulic M., 1993, Boldrin Michele, Nishimura Kazuo, Shigoka Tadashi, Yano Makoto 2000, Nishimura K., Shigoga T., Yano M, 2006). We use global bifurcation theory as understand complicated stability phenomena of a three-dimensional, economic financial models as a the well known simplified version of Lucas’s model. ( see also Benhabib J., and Nishimura K., 1979; Benhabib J., 1992; .Mattana P. and Venturi B. 1999; Fiaschi and Sordi, 2002; De Cesare L. and Sportelli M., 2004; Cai J., 2005, Neri and Venturi 2007). We analyze the trajectories of this endogenous growth two sector model for some parameters values. With the help of a numerical investigation we found a region in the parameter space that gives rise to a homoclinic orbit. We point out that, on the basis of the Shil’nikov theorem assumptions, the presence of chaos is ensured in a parameter set where the homoclinic orbit occur The economic implications of this analysis are discussed.