The objective of this study is to prove analytically the existence of the homoclinic orbit in a modified Romer model, 1990, a system with a single equilibrium point and there the existence of chaos ( see Benhabib,Perli and Xie ,1994, Benhabib et al.,.1994, Asada et al.,1998, and Slobodyan, 2005). Following Zhou T. Chen G. Yang Q., 2004, the Silnikov homoclinic orbit is studied in detail by using the undetermined coefficient method, which is presented by Zhou T. and successfully used in Chen system, in a model. We show 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.
CHAOTIC SOLUTIONS IN A CONTINUOUS TIME ENDOGENOUS GROWTH MODEL
VENTURI, BEATRICE
2012-01-01
Abstract
The objective of this study is to prove analytically the existence of the homoclinic orbit in a modified Romer model, 1990, a system with a single equilibrium point and there the existence of chaos ( see Benhabib,Perli and Xie ,1994, Benhabib et al.,.1994, Asada et al.,1998, and Slobodyan, 2005). Following Zhou T. Chen G. Yang Q., 2004, the Silnikov homoclinic orbit is studied in detail by using the undetermined coefficient method, which is presented by Zhou T. and successfully used in Chen system, in a model. We show 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.
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