Following Mulligan and Sala-i-Martin (1993) we study a general class of endogenous growth models formalized as a non linear autonomous three-dimensional differential system. We consider the abstract model. By using the Shilnikov Theorem statements, we determine the parameters space in which the condition for the existence of a homoclinic Shilnikov orbit and Smale horseshoe chaos are true. The Lucas model (1998) can be considered as an application of the general result. The series expression of the homoclinic orbit is derived by the undetermined coecient method. We show the optimality for the solutions path based on the Shilnikov Theorem. Some economic implications of this analysis are discussed. Keywords: homoclinic Shilnikov bifurcation, Smale horseshoe chaos..

Chaotic solutions in non linear economic-financial models

Venturi, Beatrice
2014

Abstract

Following Mulligan and Sala-i-Martin (1993) we study a general class of endogenous growth models formalized as a non linear autonomous three-dimensional differential system. We consider the abstract model. By using the Shilnikov Theorem statements, we determine the parameters space in which the condition for the existence of a homoclinic Shilnikov orbit and Smale horseshoe chaos are true. The Lucas model (1998) can be considered as an application of the general result. The series expression of the homoclinic orbit is derived by the undetermined coecient method. We show the optimality for the solutions path based on the Shilnikov Theorem. Some economic implications of this analysis are discussed. Keywords: homoclinic Shilnikov bifurcation, Smale horseshoe chaos..
Homoclinic; Shilnikov bifurcation; Smale horseshoe chaos
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/59025
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