In this paper we prove the existence of a homoclinic orbit in the standard Lucas’ two-sector endogenous growth model. More in detail, by the undetermined coefficient method, we analytically demonstrate that there exists a homoclinic orbit of a Sil’nikov type that connects the single equilibrium point. Furthermore, on the basis of the Shilnikov Theorem Assumptions, we find that Smale horseshoe chaos occurs both theoretically and numerically. The economic implications of this analysis are finally discussed.
CHAOTIC SOLUTIONS IN ENDOGENOUS GROWTH MODELS
MATTANA, PAOLO;VENTURI, BEATRICE
2012-01-01
Abstract
In this paper we prove the existence of a homoclinic orbit in the standard Lucas’ two-sector endogenous growth model. More in detail, by the undetermined coefficient method, we analytically demonstrate that there exists a homoclinic orbit of a Sil’nikov type that connects the single equilibrium point. Furthermore, on the basis of the Shilnikov Theorem Assumptions, we find that Smale horseshoe chaos occurs both theoretically and numerically. The economic implications of this analysis are finally discussed.
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