In this paper we use global bifurcation theory as understand complicated stability phenomena of general three-dimensional, economic financial models. ( 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, Mattana 2004, Nishimura K., Shigoga T., Yano M, 2006, Neri and Venturi 2007). We show that many theoretical results of global indeterminacy of equilibrium can be relating to systems having a homoclinic orbit biasintotic to a stationary point at some value of the parameters. These outcome depend upon the eigenvalues of the Jacobian matrix of the flow evaluated at the stationary point. We apply these results to a reduced form of the endogenous growth models due to Lucas and Romer. We use graphical and rigorous arguments to prove the existence of homoclinic orbits in these models for some parameters values. In order to understand the structure of the solutions of the systems presented, we have elaborated a numerical simulation.
NON LINEAR ECONOMIC-FINANCIAL MODELS WITH HOMOCLINIC ORBITS
VENTURI, BEATRICE
2008
Abstract
In this paper we use global bifurcation theory as understand complicated stability phenomena of general three-dimensional, economic financial models. ( 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, Mattana 2004, Nishimura K., Shigoga T., Yano M, 2006, Neri and Venturi 2007). We show that many theoretical results of global indeterminacy of equilibrium can be relating to systems having a homoclinic orbit biasintotic to a stationary point at some value of the parameters. These outcome depend upon the eigenvalues of the Jacobian matrix of the flow evaluated at the stationary point. We apply these results to a reduced form of the endogenous growth models due to Lucas and Romer. We use graphical and rigorous arguments to prove the existence of homoclinic orbits in these models for some parameters values. In order to understand the structure of the solutions of the systems presented, we have elaborated a numerical simulation.
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