Rocard´s 1941 Chaotic Relaxation Econometric Oscillator

Year: 2022

Authors: Ginoux JM., Jovanovic F., Meucci R., Llibre J.

Autors Affiliation: Aix Marseille Univ, Univ Toulon, CPT, CNRS, Marseille, France; Teluq Univ, Sch Business Adm, Quebec City, PQ, Canada; Univ Orleans, LEO, Orleans, France; CNR, Ist Nazl Ott, Largo E Fermi 6, I-50125 Florence, Italy; Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain.

Abstract: In the beginning of the Second World War, the French physicist, Yves Rocard, published a book entitled Theorie des Oscillateurs (Theory of Oscillators). In Chapter V, he designed a mathematical 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 confirmed 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 from 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 Mobius-strip and then to a toroidal attractor, according to the values of a control parameter.

Journal/Review: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Volume: 32 (3)      Pages from: 2250043-1  to: 2250043-12

More Information: The fourth author is partially supported by the Agencia Estatal de Investigacion grant PID2019-104658GB-I00, and the H2020 European Research Council Grant MSCA-RISE-2017-777911.
KeyWords: Relaxation oscillations; chaotic attractor; bifurcations; econometrics oscillator; economic crises modeling
DOI: 10.1142/S0218127422500432

Citations: 5
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