From Samuelson’s multiplier-accelerator to bifurcations and chaos in economic dynamics

This piece in the series of Milestones starts from the short, clear and highly cited paper by Samuelson (Rev Econ Stat 21(2):75–78, 1939) entitled “Interactions between the Multiplier Analysis and the Principle of Acceleration”, in which the author proposes a linear dynamic model obtained by combining the Keynesian multiplier and the principle of acceleration, together with a proper structure of time lags. Although very simple, it generated a rich and interesting literature as it provides some answers to the question of endogenous business cycles. Moreover, it raises the question of sensitivity with respect to small variations of the model’s parameters, thus sparking the attention of economists and social scientists toward studies on the qualitative theory of non-linear dynamical systems, and the related work on deterministic chaos and bifurcations which appeared between the 1960 s and 1970 s, such as the paper by Lorenz (J Atmos Sci 20:130–141, 1963) in the Journal of Atmospheric Sciences or the one by May (Nature 26:459–467, 1976) in Nature, thereby stimulating an interdisciplinary mathematical approach to dynamic complexity in physics, biology and social sciences.