Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 9-15.

• Articles • Previous Articles     Next Articles

Bifurcation and Multiple Growth Paths in an Economic Growth Model with Demographic Transition

 CAI Dong-Han, YE Hui   

  1. College of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2012-10-18 Revised:2013-11-12 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(71271158)资助.

Abstract:

In this paper, we make a further study of the model provided by Holger Sriulik[1]. It is proved that the dynamical system  which describes the model has no nonzero equilibrium  when α>α-, one nonzero equilibrium when α=α- and two equilibria, one saddle and one node when α>α- and α--α is small enough. So the dynamical system undergoes a saddle-node bifurcation at α=α-. By phase portrait analysis, we obtain that the first quadrant of y-k plane is divided into two regions by the stable manifold of the saddle point when there exists two equilibria and the economy has a Malthusian region in which all growth paths converge to the low level equilibrium and a non-Malthusian region in which the economy has normal growth path. Therefore, the economy can escape the “Malthusian poverty trap”by promoting the technological growth rate or by “big-push”which promotes the per capita income.

Key words: Bifurcation, Phase portrait analysis, Demographic transition, Multiple growth paths, Malthusian poverty trap

CLC Number: 

  • 91B62
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