MODE-LOCKING IN A FORCED BUSINESS-CYCLE

Recently, interest in nonlinear dynamics in economics and other scienc es has grown rapidly. Mode-locking is a typical phenomenon that can oc cur in systems where several oscillatory processes interact. For linea r systems, the principle of superposition applies. However, as soon as nonlinear interactions become significant, this principle ceases to b e valid, and two or more oscillatory modes will tend to adjust to one another to produce a ''locked'' solution in which one mode performs pr ecisely q cycles each time the other mode performs p cycles, with p an d q being integers. In this study we discuss mode-locking in the conte xt of the well-known Goodwin business cycle. We demonstrate how a simp le model of this cycle when perturbed by a sine wave can produce mode- locking along with the associated phenomena of a devil's staircase and so-called Arnol'd tongues. (C) 1997 Elsevier Science Inc.