Rocard's 1941 Chaotic Relaxation Econometric Oscillator [r-libre/2597]

Ginoux, Jean-Marc; Jovanovic, Franck; Meucci, Riccardo, & Llibre, Jaume (2022). Rocard's 1941 Chaotic Relaxation Econometric Oscillator. International Journal of Bifurcation and Chaos: in Applied Sciences and Engineering, 32 (3), 2250043. https://doi.org/10.1142/S0218127422500432

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Item Type:	Journal Articles
Refereed:	Yes
Status:	Published
Abstract:	In the beginning of the Second World War, the French physicist, Yves Rocard, published a book entitled Théorie des Oscillateurs (Theory of Oscillators). In Chapter V, he designed a mathemat- ical model consisting of a set of three nonlinear differential equations and allowing to account for economic cycles. Numerical integration of his model has highlighted a chaotic attractor. Its analysis with classical tools such as bifurcation diagram and Lyapunov Characteristic Exponents has con- firmed the chaotic features of its solution. It follows that Rocard’s 1941 chaotic econometric model has thus most likely preceded Lorenz’ butterfly of twenty-two years. Moreover, apart this historical discovery which upsets historiography, it is also established that this “new old” three-dimensional autonomous dynamical system is a new jerk system whose solution exhibits a chaotic attractor the topology of which varies, from a double scroll attractor to a M ̈obius-strip and then to a toroidal attractor, according to the values of a control parameter.
Official URL:	https://www.worldscientific.com/doi/10.1142/S02181...
Depositor:	Jovanovic, Franck
Owner / Manager:	Franck Jovanovic
Deposited:	24 Mar 2022 13:44
Last Modified:	01 May 2023 05:15

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