A first French episode in the renewal of nonlinear theory of economic cycles

This paper focusses on some relatively neglected French contributions to the revival of nonlinear business theory around 1980. Drawing on the formal distinction between continuous and discrete-time modeling, we investigate the mathematical and analytical features of these contributions. The Benassy model exemplifies the use of the Poincaré-Bendixon theorem to prove the existence of endogenous cycles in a simple non-Walrasian framework. The discretization of Kaldor's model by Dana and Malgrange mobilizes recent advances in bifurcation theory and chaotic dynamics developed at the same time by French scholars in dynamical systems. It is shown that both contributions build on the aggregate macroeconomic framework, but differ substantially in their objectives and ambition. Benassy mobilizes the nonlinear approach to extend his non-Walrasian theory to short-term dynamics. On the contrary, Dana and Malgrange are more interested in the operational aspects of nonlinear modeling. For the these reasons, this second line of research will contribute to further important developments in nonlinear dynamics in France, albeit in a different perspective.