Relaxation Cycle, Chaotic Dynamics and Limit Cycle: a Model with Keynesian “Flavour”

Abstract

R. Goodwin (1951) was probably the first to introduce ”relaxation cycles” in macroeconomics; Hicks’ analysis is contemporary and indeed previous (1950), both authors introducing ”non-linear accelerator” in their analysis; but Goodwin’ originality is obvious since he has used relaxation cycle and Liénard-van der Pol equations (as soon as 1933, Ph. Le Corbeiller had insisted on their interest and relevance). Further work has shown that in many cases relaxation cycle could be considered as a stable ”attractor”, a rather peculiar ”limit-cycle”, named in some cases (Chiarella 1990) ”limiting limit cycle”.