On the Huygens effect and points of hopelessness in the T.~Puu macroeconomic model

M. V. Polovinkina ; I. P. Polovinkin ; S. A. Rabeeakh

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 129-134.

Résumé

We consider the macroeconomic model proposed by T. Puu, which describes fluctuations in gross income in a given region. Under a special combination of savings and investment rates, income deviations occur only for a finite period of time, after which the income returns to a stationary state. In mathematical physics, this effect is called the Huygens effect (principle). Results of the study of the model by statistical methods allow one to speak about the plausibility of the hypothesis about the presence of the Huygens effect in certain periods of the history of the Russian economy. The question on the structure of the set of stationary zeros of nontrivial solutions of a stationary equation is considered.

Détail

Mots-clés : income distribution model, Huygens principle, Cauchy problem, dependence domain, stationary zeros of the solution.

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