Haxholdt, Christian with Christian Kampmann, "Entrainment in a disaggregated Economic Long Wave Model", 1993

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This paper investigates how mode-locking and other highly nonlinear dynamic phenomena arise through the interaction of two capital-producing sectors in a disaggregated economic long-wave model. One sector might represent the construction of building and infrastructure capital with long lifetimes while the other represents production of machinery, computers, etc. with much shorter lifetimes. Due to the positive feedback associated with capital self-ordering, each sector in isolation produces a self-sustained oscillation with a period and amplitude determine 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 ratio 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 strength of the coupling between sectors. Besides mode-locking and quasi-periodic behavior, the observed phenomena includes cascades of period-doubling bifurcations, chaos, and intermittency. When the difference in capital lifetimes is very large, the system behaves like a one-sector model with a reduced capital content of production: Only one oscillatory mode remains, and it is much less pronounced than in the original one-sector model.

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