Classical economic growth theory: a global bifurcation analysis

Abstract

This paper presents a global birfurcation analysis for the classical demoeconomic growth model, in which household income must exceed a threshold before children can survive to adulthood and/or until adults are willing to substitute childrearing for consumption. Convergence to a stationary or steady growth state occurs genetically, but persistent fluctuations are also generic (chaotic or cyclic) around a stationary state, or with expanding amplitude around a growth trend, when technology is advancing. Population can also overshoot its domain of viability, experience a drastic contraction, and then die out. These varied possibilities illustrate global dynamic analysis and may help explain some of the vicissitudes of human societies described in the archaeological and historical records.