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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

    as
    1. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    2. Li Chen & Jianhui Huang, 2015. "Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1112-1135, December.
    3. 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.
    4. Hwan C. Lin & L. F. Shampine, 2018. "R&D-based Calibrated Growth Models with Finite-Length Patents: A Novel Relaxation Algorithm for Solving an Autonomous FDE System of Mixed Type," Computational Economics, Springer;Society for Computational Economics, vol. 51(1), pages 123-158, January.
    5. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 16-24.
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    7. repec:hal:pseose:hal-01175922 is not listed on IDEAS
    8. Hwan C. Lin, 2018. "Erratum to: Computing Transitional Cycles for a Deterministic Time-to-Build Growth Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 697-697, March.
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    Full references (including those not matched with items on IDEAS)

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