Limit Cycles in Higher Dimension - The Effect of Time Lags on Goodwin’s Model of Cyclical Growth

In the last two chapters we have applied some of the nonlinear techniques of chapter two to various macroeconomic models which mathematically reduce to a system of two nonlinear differential equations. In this chapter we shall illustrate the analysis of a three dimensional nonlinear system by use of the centre manifold concepts discussed in section 2.7. A convenient model on which to illustrate these concepts is Goodwin’s (1967) model of cyclical growth. This model for some considerable time received scant attention in the economics literature, apart from the contribution of Desai (1973). However recent interest in theories of economic cycles has led to a resurgence of activity on Goodwin’s model, see e.g. Goodwin et al., (1984), Blatt (1983), van der Ploeg (1983), Medio (1979), and Vellupillai (1979).