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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Hopf Bifurcation in an Augmented Solow Model with Two Delays

Journal of Applied Nonlinear Dynamics 11(2) (2022) 459--471 | DOI:10.5890/JAND.2022.06.013

S. ElFadily, A. Kaddar, K. Najib

LERMA, Mohammadia School of engineering, Mohammed V University, Rabat, Morocco

LABSIPE, National School of Applied Sciences, Chouab Doukkali Univerity, El Jadida, Morocco

LERMA, National High School of Mines, Rabat, Morocco

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Abstract

The relationship between demographic change and economic growth is a topical subject that has always attracted the interest of researchers. Given the fluctuations in economic and demographic variables, studing and analysing the direct relationship (cause and effect relationship) between economic growth and population is complex one. In the same line, the present paper aims at analising this relationships by increasing the dynamic of the Solow economic growth model with three demographic variables and considering two time delays. The study investigates the stability of positives equilibria and the existence of limit cycles by using Hopf bifurcation theorem. The role of the time delays in the variables of the proposed model and possible links between them at various phases (stability, limit cycle and instability) are also examined in this study. Finally, to illustrate our analytical results, some numerical simulations are presented.

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