关键词: 分歧, 相图分析, 人口转变, 多重增长路径, Malthus贫困陷阱

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