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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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- Rocard’s 1941 Chaotic Relaxation Econometric Oscillator IJBC 2022.pdf
Content : Published Version |
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Item Type: | Journal Articles |
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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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