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

Ginoux, Jean-Marc; Jovanovic, Franck; Meucci, Riccardo et 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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Catégorie de document :	Articles de revues
Évaluation par un comité de lecture :	Oui
Étape de publication :	Publié
Résumé :	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.
Adresse de la version officielle :	https://www.worldscientific.com/doi/10.1142/S02181...
Déposant:	Jovanovic, Franck
Responsable :	Franck Jovanovic
Dépôt :	24 mars 2022 13:44
Dernière modification :	01 mai 2023 05:15

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