具有人口转变经济增长模型中的分歧和多重增长路径  

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

作　　者：蔡东汉[1] 叶辉[1] 

机构地区：[1]武汉大学数学统计学院,武汉430072

出　　处：《数学物理学报（A辑）》2014年第1期9-15,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金(71271158)资助

摘　　要：该文对Holger Sriulik^([1])给出的模型作了进一步的研究.证明在给定的技术水平下,描述模型的动力系统出现鞍结定分歧.当模型存在两个平衡点时,鞍点的稳定流形将y-k平面的第一像限分成两个区域,其左边为Malthus区域,该区域的所有轨道收敛于一个低水平的平衡点;其右边为非Malthus区域,该区域的轨道为正常的经济增长路径.经济可以通过提高技术水平或提高人均收入的"大冲击"方法逃离"Malthus贫困陷阱".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 ā 〉 O, one nonzero equilibrium when a = ā and two equilibria, one saddle and one node when a 〈 ā and ā - a is small enough. So the dynamical system undergoes a saddle-node bifurcation at a - ā. 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.

关 键 词：分歧 相图分析 人口转变 多重增长路径 Malthus贫困陷阱 

分 类 号：O192[理学—数学] O232[理学—基础数学]