Geodesic
On stabilization of an automaton model of migration processes
Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 56-71.

Voir la notice de l'article provenant de la source Math-Net.Ru

A dynamic system of cities with migrants is considered. The wage function is each city depends on the number of migrants in the city. The system is modeled by an automaton whose state is the vector consisting of the numbers of migrants in the cities. The transition function of the automaton reflects the conditions for transfers of migrants between cities. The system stabilizes if the moves are stopped at some point. We find conditions for stabilization of such system depending on the restrictions on the wage function and the automaton transition function. It is shown that if the functions of wages are strictly decreasing, if their ranges are disjoint, and if the transition function is defined so that a migrant moves to another city if and only if its salary increases, then the system necessarily stabilizes and its final state depends only on the total number of migrants and does not depend on their initial distribution over the cities. However, if the transition function is changed so that a migrant moves also if its salary is preserved, but the total wages in all cities are increased, then a monotonous decrease in the wage functions is sufficient for stabilization of the system.
Keywords: automaton modelling of migration processes, stabilization of dynamic systems. 
@article{DM_2019_31_1_a3,
     author = {D. I. Vasilyev and \`E. \`E. Gasanov and V. B. Kudryavtsev},
     title = {On stabilization of an automaton model of migration processes},
     journal = {Diskretnaya Matematika},
     pages = {56--71},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_1_a3/}
}
TY  - JOUR
AU  - D. I. Vasilyev
AU  - È. È. Gasanov
AU  - V. B. Kudryavtsev
TI  - On stabilization of an automaton model of migration processes
JO  - Diskretnaya Matematika
PY  - 2019
SP  - 56
EP  - 71
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2019_31_1_a3/
LA  - ru
ID  - DM_2019_31_1_a3
ER  - 
%0 Journal Article
%A D. I. Vasilyev
%A È. È. Gasanov
%A V. B. Kudryavtsev
%T On stabilization of an automaton model of migration processes
%J Diskretnaya Matematika
%D 2019
%P 56-71
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2019_31_1_a3/
%G ru
%F DM_2019_31_1_a3
D. I. Vasilyev; È. È. Gasanov; V. B. Kudryavtsev. On stabilization of an automaton model of migration processes. Diskretnaya Matematika, Tome 31 (2019) no. 1, pp. 56-71. http://geodesic.mathdoc.fr/item/DM_2019_31_1_a3/

[1] Kauffman S.; Weinberger E., “The NK model of rugged fitness landscapes and its application to the maturation of the immune response”, J. Theor. Biology, 141:2 (1989), 211–245 | DOI

[2] Kauffman S, “Homeostasis and differentiation in random genetic control networks”, Nature, 224:5215 (1969), 177–178 | DOI

[3] Zholbarysov M.Zh., Shutkin Yu.S., “Problema stabilizatsii v bulevykh setyakh”, Intellektualnye sistemy, 21:4 (2017), 130–143

[4] Shutkin Yu.S., “O probleme stabilizatsii bulevykh setei”, Intellektualnye sistemy, 20:3 (2016), 85–87 | MR

[5] Kazakov I.B., “Struktura grafa na mnozhestve perestanovok $S_n$, zadavaemaya modelyu oshibki v skrytom kanale perestanovki paketov”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:2 (2018), 53–79

[6] Gasanov E.E., “O funktsionalnoi slozhnosti dvumernoi zadachi o dominirovanii”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:4 (2017), 102–114

[7] Ananev K.Yu., “O metodakh postroeniya LDPC-kodov s zadannymi kharakteristikami”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:3 (2017), 107–119

[8] Ischenko R.A., “Grafy gruppovykh avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:2 (2017), 111–116

[9] Vedyushkina (Fokicheva) V., Ivanov A., Tuzhilin A., Fomenko A., “Kompyuternye modeli v geometrii i dinamike”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:1 (2017), 164–191

[10] Chernova Yu.G., “O slozhnostnoi funktsii vremeni samoochischeniya legkikh pri nekotorykh patologiyakh”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:4 (2016), 143–152

[11] Ischenko R.A., “O razlozhenii grafov na podgrafy spetsialnogo vida”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:4 (2016), 184–192

[12] Gasanov E.E., Pletnev A.A., “Modelirovanie dinamicheskikh baz dannykh”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 146–150 | MR

[13] Pletnev A.A., “Minimalno vozmozhnyi po stepeni vetvleniya informatsionnyi graf s radiusom vidimosti odin, obrabatyvayuschii proizvolnyi potok zaprosov k dinamicheskoi baze dannykh”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:1 (2016), 223-254 | MR

[14] Shulgina E.A., “Otsenka parametrov biregulyarnykh dvudolnykh grafov”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:1 (2016), 255–263 | MR

[15] Samonenko I.Yu., “O kolichestve regulyarnykh yazykov, predstavimykh v gruppovykh giperavtomatakh”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:2 (2018), 113–123

[16] Chasovskikh A.A., “Problema polnoty v klassakh lineinykh avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:2 (2018), 151–154

[17] Ivanov I.E., “Ob avtomatnykh funktsiyakh s magazinnoi pamyatyu”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:1 (2018), 39–110

[18] Panteleev P.A., “Ob obobschenii teoremy Mura”, Intellektualnye sistemy. Teoriya i prilozheniya, 22:1 (2018), 151–154 | MR

[19] Ronzhin D.V., “Lineinye avtomaty nad polem ratsionalnykh chisel”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:4 (2017), 144–155

[20] Rodin S.B., “O svoistvakh kodirovaniya sostoyanii avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:1 (2017), 97–111

[21] Ivanov I.E., “Otsenka dliny perioda vykhodnoi posledovatelnosti dlya avtonomnogo avtomata s magazinnoi pamyatyu s odnobukvennym magazinom”, Intellektualnye sistemy. Teoriya i prilozheniya, 21:1 (2017), 112–148

[22] Volkov N.Yu., Ushakova V.V., “O vychislimosti funktsii kollektivami iz dvukh avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:4 (2016), 21–24

[23] Gukasyan V.G., “Vzaimosvyaz avtomatnykh modelei bezopasnykh informatsionnykh sistem bez skrytykh kanalov peredachi dannykh”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:4 (2016), 30–36

[24] Babin D.N., “Klass avtomatov s superpozitsiyami, ne rasshiryayuschiisya do predpolnogo”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 155–166 | MR

[25] Ivanov I.E., “Uluchshenie nizhnei otsenki na maksimalnuyu dlinu perioda vykhodnoi posledovatelnosti avtonomnogo avtomata s magazinnoi pamyatyu”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 167–183

[26] Chasovskikh A.A., “O polnote v klasse lineinykh 2-adicheskikh avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:4 (2016), 209–227

[27] Babin D.N., Letunovskii A.A., “Algoritmicheski razreshimye sluchai v zadache vyrazimosti avtomatov otnositelno superpozitsii”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 96–100

[28] Babin D.N., Parkhomenko D.V., “O multimnozhestve vykhodnykh slov konechnogo avtomata”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 101–102

[29] Morozov S.S., “O slozhnosti modelirovaniya avtomatami regulyarnykh sobytii”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 112–114

[30] Rodin S.B., “Neizbytochnye kodirovaniya avtomatov”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 115–119 | MR

[31] Chasovskikh A.A., “Sravnenie operatorov zamykaniya v klasse lineino-avtomatnykh funktsii”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:3 (2016), 120–124

[32] Mironov A.M., “Osnovnye ponyatiya teorii veroyatnostnykh avtomatov (chast 2)”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:2 (2016), 283–330 | MR

[33] Rodin S.B., “O svyazi lineino realizuemykh avtomatov i avtomatov s maksimalnoi variativnostyu otnositelno kodirovaniya sostoyanii”, Intellektualnye sistemy. Teoriya i prilozheniya, 20:2 (2016), 337–348 | MR

[34] Vasilev D.I., “O stabilizatsii odnoi dinamicheskoi sistemy, svyazannoi s avtomatnym modelirovaniem migratsionnykh protsessov”, Intellektualnye sistemy. Teoriya i prilozheniya, 19:3 (2015), 27–37 | MR