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Open AccessArticle

Equilibrium and Stability of Entropy Operator Model for Migratory Interaction of Regional Systems

by Yuri S. Popkov 1,2,3,4,* and Leo van Wissen 4,5,6
1
Institute for Systems Analysis of FRC CSC of RAS, Moscow 119333, Russia
2
Institute of Control Sciences of Russian Academy of Sciences, Moscow 117997, Russia
3
National Research, University Higher School of Economics, Moscow 125319, Russia
4
Department of Engineering, Haifa University, Karmiel 2161002, Israel
5
Netherlands Interdisciplinary Demographic Institute, P.O. Box 11650, 2502 AR Den Haag, The Netherlands
6
Population Research Centre, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(2), 130; https://doi.org/10.3390/math7020130
Received: 26 December 2018 / Revised: 21 January 2019 / Accepted: 26 January 2019 / Published: 29 January 2019
(This article belongs to the Section Mathematics and Computer Science)
In this paper, we develop a dynamic model for migratory interaction of regional systems that is based on an entropy operator. Next, we study the properties of this operator and establish the existence of a unique singular point in the dynamic entropy model. Here, we use monotonicity property of entropy operator on corresponding vector interval. We study Lyapunov stability of a dynamic system with entropy operator. Stability conditions have been obtained in terms of eigenvalues of linearized system’s matrix. Finally, we give an illustrative example for migratory interaction of regional systems. View Full-Text
Keywords: migration; regional mobility; prior probabilities of migratory movements; dynamic system with entropy operator; monotonic operator; stability in small; singular point migration; regional mobility; prior probabilities of migratory movements; dynamic system with entropy operator; monotonic operator; stability in small; singular point
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Popkov, Y.S.; van Wissen, L. Equilibrium and Stability of Entropy Operator Model for Migratory Interaction of Regional Systems. Mathematics 2019, 7, 130.

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