Some Economic Dynamics Problems for Hybrid Models with Aftereffect

Eugene Bravyi, Vladimir Maksimov and Pyotr Simonov
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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

Mathematics, 2020, vol. 8, issue 10, 1-30

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.

Keywords: economic dynamics; boundary value problems; control problems; attainability; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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