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

Carlo Bianca | Zendy; Массимилиано Феррара | Zendy; Luca Guerrini | Zendy

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

Author(s) -

Carlo Bianca,

Массимилиано Феррара,

Luca Guerrini

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/901014

Subject(s) - mathematics , center manifold , generalization , hopf bifurcation , stability (learning theory) , argument (complex analysis) , period doubling bifurcation , order (exchange) , bifurcation , exponential stability , steady state (chemistry) , manifold (fluid mechanics) , mathematical analysis , mathematical economics , nonlinear system , economics , computer science , biochemistry , chemistry , physics , finance , quantum mechanics , machine learning , mechanical engineering , engineering

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.

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