Rocard's 1941 chaotic relaxation econometric oscillator
Ginoux, Jean-Marc (Centre National de la Recherche Scientifique. Université de Toulon)
Jovanovic, Franck (Teluq University. Université d'Orléans. School of Business Administration)
Meucci, Riccardo (Consiglio Nazionale Delle Ricerche. Istituto Nazionale di Ottica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2022
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 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 Möbius-strip and then to a toroidal attractor, according to the values of a control parameter.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Relaxation oscillations ; Chaotic attractor ; Bifurcations ; Econometrics oscillator ; Economic crises modeling
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 3 (March 2022) , art. 2250043, ISSN 1793-6551

DOI: 10.1142/S0218127422500432

Postprint 11 p, 569.3 KB

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