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Optimisation of Cycling Trends in Hamiltonian Systems of Economic Growth Models

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  • Alexander Mikhailovich Tarasyev

    (Krasovskii Institute of Mathematics and Mechanics of Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya Street, 620990 Yekaterinburg, Russia
    Research Laboratory on the Problems of University Development, Research Department, Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia
    These authors contributed equally to this work.)

  • Anastasia Alexandrovna Usova

    (Krasovskii Institute of Mathematics and Mechanics of Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya Street, 620990 Yekaterinburg, Russia
    These authors contributed equally to this work.)

  • Alexander Alexandrovich Tarasyev

    (Research Laboratory on the Problems of University Development, Research Department, Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia
    These authors contributed equally to this work.)

Abstract

The paper analyses dynamical growth models predicting the cyclic development of investigated economic factors. The provided research deals with an optimal control problem based on the economic growth model with the production function of Cobb–Douglas type. Following the Pontryagin maximum principle, we derived the Hamiltonian system and conducted its qualitative analysis, which reveals conditions for the cyclic behaviour of the optimal solutions around the isolate steady state. Numerical experiments visually illustrated the obtained results by demonstrating a phase portrait corresponding to a steady state of the focal type.

Suggested Citation

  • Alexander Mikhailovich Tarasyev & Anastasia Alexandrovna Usova & Alexander Alexandrovich Tarasyev, 2023. "Optimisation of Cycling Trends in Hamiltonian Systems of Economic Growth Models," Mathematics, MDPI, vol. 11(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2452-:d:1155833
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