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International Journal of Differential Equations
Volume 2019, Article ID 7609828, 8 pages
https://doi.org/10.1155/2019/7609828
Research Article

Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand

1Mohammadia School of Engineering, Mohammed V University in Rabat, Rabat, Morocco
2Laboratoire de Finance, Entrepreneuriat, et Développement, Faculté des Sciences Juridiques, Economiques et Sociales de Salé, Université Mohammed V de Rabat, Sala Al Jadida, Morocco
3Department of Applied Mathematics, National School of Mineral Industry, Rabat, Morocco

Correspondence should be addressed to Sanaa ElFadily; moc.liamg@aanasylidafle

Received 11 February 2019; Revised 24 April 2019; Accepted 8 May 2019; Published 2 June 2019

Academic Editor: Patricia J. Y. Wong

Copyright © 2019 Sanaa ElFadily 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.

Linked References

  1. R. F. Harrod, “An essay in dynamic theory,” The Economic Journal, vol. 49, no. 193, pp. 14–33, 1939. View at Publisher · View at Google Scholar
  2. E. D. Domar, “Expansion and employment,” in The American Economic Review, vol. 37, pp. 34–55, American Economic Association, 1947. View at Google Scholar
  3. C. Gustav, “Capital and income in the money economy,” in The Theory of Social Economy, p. 5117, Augustus M. Kelley, New York, NY, USA, 1967. View at Google Scholar
  4. R. M. Solow, “A contribution to the theory of economic growth,” The Quarterly Journal of Economics, vol. 70, no. 1, pp. 65–94, 1956. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Hallegatte, M. Ghil, P. Dumas, and J.-C. Hourcade, “Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics,” Journal of Economic Behavior & Organization, vol. 67, no. 1, pp. 57–77, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Cai, “Multiple equilibria and bifurcations in an economic growth model with endogenous carrying capacity,” International Journal of Bifurcation and Chaos, vol. 20, no. 11, pp. 3461–3472, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  7. D. Cai, “An economic growth model with endogenous carrying capacity and demographic transition,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 432–441, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. L. Guerrini and M. Sodini, “Nonlinear dynamics in the solow model with boundedpopulation growth and time-to-build technology,” Abstract and Applied Analysis, vol. 2013, Article ID 836537, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. ElFadily, A. Kaddar, and K. Najib, “Dynamics of a delayed solow model with effective labor demand,” Journal of Advances in Applied Mathematics, vol. 1, no. 3, pp. 175–182, 2016. View at Publisher · View at Google Scholar
  10. V. Jablanovic, “A chaotic economic growth model and the agricultural share of an output,” Journal of Agricultural Sciences, Belgrade, vol. 50, no. 2, pp. 207–216, 2005. View at Publisher · View at Google Scholar
  11. D. Guégan, “Chaos in economics and finance,” Annual Reviews in Control, vol. 33, no. 1, pp. 89–93, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Akhmet, Z. Akhmetova, and M. O. Fen, “Chaos in economic models with exogenous shocks,” Journal of Economic Behavior & Organization, vol. 106, pp. 95–108, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. L. Zhao and Z. Zhao, “Stability and Hopf bifurcation analysis on a nonlinear business cycle model,” Mathematical Problems in Engineering, vol. 2016, Article ID 2706719, 15 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  14. A. Sulaiman and M. Sadly, “Agricultural growth modeling based on nonlinear dynamical system,” in Proceedings of the International Conference on Advanced Computer Science and Information Systems, IEEE, Depok, Indonesia, 2013.
  15. L. Guerrini, “Hopf bifurcation in a delayed Ramsey model with Von Bertalanffy population law,” International Journal of Differential Equations and Applications, vol. 11, no. 1, pp. 81–86, 2012. View at Google Scholar
  16. D. Cai, H. Ye, and L. Gu, “A generalized solow-swan model,” Abstract and Applied Analysis, vol. 2014, Article ID 395089, 8 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. M. Bohner, J. Heim, and A. Liu, “Qualitative analysis of a Solow model on time scales,” Journal of Concrete and Applicable Mathematics, vol. 13, no. 3-4, pp. 183–197, 2015. View at Google Scholar · View at MathSciNet
  18. A. Akaev, “Nonlinear differential equation of macroeconomic dynamics for long-term forecasting of economic development,” Applied Mathematics, vol. 9, no. 5, pp. 512–535, 2018. View at Publisher · View at Google Scholar
  19. Y. Basnett and R. Sen, What Do Empirical Studies Say about Economic Growth and Job Creation in Developing Countries? London, UK, ODI, 2013.
  20. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, vol. 112 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2nd edition, 1998. View at MathSciNet
  21. C. W. Cobb and P. H. Douglas, “A theory of production,” American Economic Review, vol. 18, no. 1, pp. 139–165, 1928. View at Google Scholar
  22. J. K. Hale, Introduction to Functional-Differential Equations, Springer-Verlag, New York, NY, USA, 1993. View at Publisher · View at Google Scholar · View at MathSciNet