Skip Navigation Links
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

Download Full Text PDF

 

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.

References

  1. [1]  Cypher, J.M. and Dietz, J.L. (2008), The Process of Economic Development (3rd Revised ed.), Routledge, ISBN 0-415-77104-8, 1-640.
  2. [2]  Hayami, Y. and Yoshihisa, G, (2005), Development economics: from the poverty to the wealth of nations (3, illustrated ed.), Oxford University Press, 1-430.
  3. [3]  Hirschman, A.O (1969), The Strategy of Economic Development, in Agarwal, A.N. and Singh, S.P.(eds), Accelerating Investment in Developing Economies (London Oxford Press).
  4. [4]  Singer, H. (1958), The Concept of Balanced Growth and Economic Development; Theory and Facts, University of Texas Conference on Economic Development.
  5. [5]  Streeten, P. (1961), Unbalanced Growth, Economic Integration, Sythoff, Leiden (Pays-Bas), Reprinted in A. N. Agarwala and S. P. Singh, (eds.), Accelerating Investment in Developing Economies (London: Oxford University Press, 1969).
  6. [6]  Fleming, J.M. (1962), Domestic financial policies under fixed and floating exchange rates, IMF Staff Papers, 9, Reprinted in International Finance: New York, Penguin Books, 369-379.
  7. [7]  Harrod, R.F. (1939), An Essay in Dynamic Theory, The Economic Journal, 49(193), 14-33.
  8. [8]  Domar, E., (1946), Capital Expansion, Rate of Growth, and Employment, Econometrica, 14(2), 137-147.
  9. [9]  Solow, R. (1956), A contribution to the theory of economic growth, The Quarterly Journal of Economics, The MIT Press, 70(1), 65-94.
  10. [10]  Kaldor, N, (1957), A model of Economic Growth, Economic Journal, 67, CrossRef. Google Scolar, 591-624.
  11. [11]  ElFadily, S., Kaddar, A., and Najib, K. (2016), Dynamics of a Delayed Solow Model with Effective Labor Demand, Journal of Advances in Applied Mathematics, 1(3).
  12. [12]  Kaddar, A., Sahbani, S., and Talibi, A. (2017), Hopf Bifurcation in a Delayed Solow-Verhulst Model, Research in Applied Mathematics, 1, 1-10.
  13. [13]  Hallegatte, S., Ghil, M., Dumas, P., and Hourcade, J.C, (2008), Business cycles, bifurcations and chaos in a neoclassical model with investment dynamics, Journal of Economic Behavior and Organization, 67(1), 57�77.
  14. [14]  Cobb, C. and Douglas, P. (1928), A theory of production, The American Economic Review, 18(1), 139�165, 1-5.
  15. [15]  Hale, J.K. and Verduyn Lunel, S.M, (1993), Introduction to Functional Differential Equations, Springer- Verlag, New York.
  16. [16]  Kuang, Y. (1993), Delay differential equations with applications in population dynamics, Boston: Academic Press.
  17. [17]  Gori, L., Guerrini, L., and Sodini, M. (2016), A model of economic growth with physical and human capital: The role of time delays, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(9), 093118.
  18. [18]  Bianca, C. and Luca Guerrini, L. (2014), Existence of Limit Cycles in the Solow Model with Delayed-Logistic Population Growthqa, The Scientific World Journal. Article ID 207806, 1-8.
  19. [19]  ElFadily, S., Kaddar, A., and Najib, K. (2019), Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand, International Journal of Differential Equations, 2019, 1-8.
  20. [20]  ElFadily, S., Najib, K., and Kaddar, A. (2021), Stability Analysis of Bifurcated Limit Cycles in a Labor Force Evolution Model, Nonlinear Analysis, Problems, Applications and Computational Methods, Copyright HolderName Springer Nature Switzerland AG, 168.
  21. [21]  Kalecki, M. (1935), A macrodynamic theory of business cycles, Econometrica, 3(3), 327�344.
  22. [22]  Kuznetsov, Y.A. (1998), Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, Springer, 112, NewYork, (2nd edition).