Entrainment in a disaggregated economic long wave model

This paper investigates how mode-locking and other nonlinear dynamic phenomena arise through the interaction of two capital-producing sectors in a disaggregated economic long wave model. Each sector in isolation produces a self-sustained oscillation with a period and amplitude determined by the characteristics of that sector. However, the sectors interact through their mutual dependence on each other's output for their own production. When this coupling is accounted for, the two sectors tend to synchronize or lock together with a rational proportion between the periods. While keeping the aggregate equilibrium characteristics of the system constant, we study how this locking occurs as a function of the difference in capital lifetimes and as a function of the strength of the coupling between the sectors. Besides mode-locking and quasi-periodic behavior, the observed phenomena include cascades of period-doubling bifurcations, chaos, and intermittency. When the difference in capital lifetimes is very large, the coupled system tends to behave like a one-sector model with a reduced capital content of production.