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Abstract and Applied Analysis
Volume 2013, Article ID 901014, 10 pages
Research Article

The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

1Dipartimento di Scienze Matematiche, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2Department of Law and Economics, University Mediterranea of Reggio Calabria and CRIOS University Bocconi of Milan, Via dei Bianchi 2, 89127 Reggio Calabria, Italy
3Department of Management, Polytechnic University of Marche, 60121 Ancona, Italy

Received 14 August 2013; Accepted 1 November 2013

Academic Editor: Constantin Udriste

Copyright © 2013 Carlo Bianca et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.