Geodesic
Gravitational model of population dynamics
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 80-93 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the author's mathematical model of population dynamics of territories, taking into account the migration between the territories. The model is a system of ordinary differential equations with constant coefficients. The main idea of the presented modelling is to take into account the migration interactions of territories in the form of nonlinear terms (they are the pair products of phase variables of the territories population). On the one hand, the approach allows to consider the model as a variant of expanding the gravitational approach in migration studies. On the other hand, this approach allows to apply the approaches of mathematical biology, which are successfully used in econophysics and sociodynamics. In order to verify the model, we use statistical data on population and migration between federal districts of the Russian Federation. The results of the modelling show the significance of the "repulsion" of migrants arriving in the Central and North-Western federal districts, mainly in the nearby regions (Southern, North Caucasian and Volga federal districts). Model evaluations of the migration balance are obtained. The evaluations exceed statistical ones by dozens of times and, to all appearances, describe the "latent" migration of the population, covering both long-term and short-term movements. An analysis of the change in the stationary values of the population for a linear change in the parameters is carried out. It is shown that there are such values of the parameters of migration attractiveness of the Russian Federation federal districts, under which the population increases both in the whole in the Russian Federation and in individual districts. It is established that such changes can occur due to significant differences in the opportunities, which are "provided" by different federal districts for migrants (e.g., living and working conditions, upbringing and education of children, etc.), and intra-Russian migration.
Keywords: gravitational approach; migration; population; federal districts of the Russian Federation; ordinary differential equations. 
@article{VYURU_2017_10_3_a6,
     author = {M. Yu. Khavinson and M. P. Kulakov},
     title = {Gravitational model of population dynamics},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {80--93},
     year = {2017},
     volume = {10},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a6/}
}
TY  - JOUR
AU  - M. Yu. Khavinson
AU  - M. P. Kulakov
TI  - Gravitational model of population dynamics
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2017
SP  - 80
EP  - 93
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a6/
LA  - en
ID  - VYURU_2017_10_3_a6
ER  - 
%0 Journal Article
%A M. Yu. Khavinson
%A M. P. Kulakov
%T Gravitational model of population dynamics
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2017
%P 80-93
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a6/
%G en
%F VYURU_2017_10_3_a6
M. Yu. Khavinson; M. P. Kulakov. Gravitational model of population dynamics. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 80-93. http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a6/

[1] Mishchuk S. N., “Peculiarities of International Labour Migration from China to Russia (on the Example of the Far East Federal District”, Economy of Region, 38:2 (2014), 194–202 (in Russian) | DOI

[2] Mischuk S. N., “Retrospective Analysis of Migration in Jewish Autonomous Region”, Regional Problem, 18:3 (2015), 74–81 (in Russian)

[3] Motrich E. L., Naiden S. N., “Migration Processes in the Socioeconomic Development of the Far East”, Studies on Russian Economic Development, 26:5 (2015), 491–498 | DOI

[4] Khavinson M. Yu., Kulakov M. P., Mishchuk S. N., “Prediction of Foreign Labor Migration Dynamics at the Regional Level”, Studies on Russian Economic Development, 24:2 (2013), 170–178 | DOI

[5] Romanovskij M. Ju., Romanovskij Ju. M., An Introduction to Econophysics: Statistical and Dynamic Models, Izhevsk Institute of Computer Science, M.–Izhevsk, 2012, 340 pp.

[6] Khavinson M. Yu., “Econophysics: from Finance Analysis to the Fate of Mankind”, Spatial Economics, 2015, no. 1, 144–166 (in Russian) | DOI

[7] Vasilenko P. V., “Gravitation Power and Migratory Mobility of the Regions Population”, Immanuel Kant Baltic Federal University's Vestnik. Series: Natural and Medical Sciences, 2013, no. 7, 153–157

[8] Drapkin I. M., Mariev O. S., Chukavina K. V., “Gravity Approach towards the Empirical Estimation of Foreign Direct Investment Factors in Russian Economy”, Bulletin of Ural Federal University. Series: Economics and Management, 2014, no. 6, 58–66 (in Russian)

[9] Kaukin A. S., “Features of Empirical Estimates of the Gravity Model of Russian Foreign Trade”, Russian Foreign Economic Bulletin, 2013, no. 4, 71–84 (in Russian)

[10] Chernavskii D. S., Synergetics and Information: Dynamical Theory of Information, URSS, M., 2016, 304 pp. | MR

[11] Riznichenko G. Ju., Rubin A. B., Biophysical Dynamics of Production Processes, Izhevsk Institute of Computer Science, M.–Izhevsk, 2004, 464 pp. (in Russian)

[12] Frisman E. Ya., Neverova G. P., Revutskaya O. L., “Complex Dynamics of the Population with a Simple Age Structure”, Ecological Modelling, 222:12 (2011), 1943–1950 | DOI

[13] Lobanova E. V., Medvedeva N. B., “Smooth Models of Biological Populations”, Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 7:2 (2014), 55–65 (in Russian) | DOI | Zbl

[14] Kulakov M. P., Neverova G. P., Frisman E. Ya., “Multistability in Dynamic Models of Migration Coupled Populations with an Age Structure”, Russian Journal of Nonlinear Dynamics, 10:4 (2014), 407–425 (in Russian) | DOI

[15] Weidlich W., Sociodynamics: a Systematic Approach to Mathematical Modelling in the Social Sciences, CRC Press, Boca Raton, 2000, 392 pp. | MR

[16] The Official Website of the Federal State Statistics Service, , 2016 (accessed 5 May 2016) [Официальный сайт Федеральной службы государственной статистики, (дата обращения: 05.05.2016)] http://www.gks.ruhttp://www.gks.ru

[17] The Demographic Yearbook of Russia: 2015, Statistical Yearbook, Rosstat, M., 2015, 263 pp.