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Some Economic Dynamics Problems for Hybrid Models with Aftereffect

Author

Listed:
  • Eugene Bravyi

    (Scientific Center of Functional Differential Equations, Perm National Research Polytechnic University, 614990 Perm, Russia)

  • Vladimir Maksimov

    (Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990 Perm, Russia)

  • Pyotr Simonov

    (Department of Information Systems and Mathematical Methods in Economics, Perm State University, 614990 Perm, Russia)

Abstract

In this paper, we consider a class of economic dynamics models in the form of linear functional differential systems with continuous and discrete times (hybrid models) that covers many kinds of dynamic models with aftereffect. The focus of attention is periodic boundary value problems with deviating argument, control problems with respect to general on-target vector-functional and questions of stability to solutions. For boundary value problems, some sharp sufficient conditions of the unique solvability are obtained. The attainability of on-target values is under study as applied to control problems with polyhedral constraints with respect to control, some estimates of the attainability set as well as estimates to a number of switch-points of programming control are presented. For a class of hybrid systems, a description of asymptotic properties of solutions is given.

Suggested Citation

  • Eugene Bravyi & Vladimir Maksimov & Pyotr Simonov, 2020. "Some Economic Dynamics Problems for Hybrid Models with Aftereffect," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1832-:d:431032
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    References listed on IDEAS

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    1. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
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