Geodesic
Asymptotic analysis of the “authority-society” model in case of two stable authority profiles
Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 23-34 
M. G. Dmitriev; G. S. Joukova; A. P. Petrov. Asymptotic analysis of the “authority-society” model in case of two stable authority profiles. Matematičeskoe modelirovanie, Tome 16 (2004) no. 5, pp. 23-34. http://geodesic.mathdoc.fr/item/MM_2004_16_5_a1/
@article{MM_2004_16_5_a1,
     author = {M. G. Dmitriev and G. S. Joukova and A. P. Petrov},
     title = {Asymptotic analysis of the {\textquotedblleft}authority-society{\textquotedblright} model in case of two stable authority profiles},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {23--34},
     year = {2004},
     volume = {16},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_5_a1/}
}
TY  - JOUR
AU  - M. G. Dmitriev
AU  - G. S. Joukova
AU  - A. P. Petrov
TI  - Asymptotic analysis of the “authority-society” model in case of two stable authority profiles
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 23
EP  - 34
VL  - 16
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_5_a1/
LA  - ru
ID  - MM_2004_16_5_a1
ER  - 
%0 Journal Article
%A M. G. Dmitriev
%A G. S. Joukova
%A A. P. Petrov
%T Asymptotic analysis of the “authority-society” model in case of two stable authority profiles
%J Matematičeskoe modelirovanie
%D 2004
%P 23-34
%V 16
%N 5
%U http://geodesic.mathdoc.fr/item/MM_2004_16_5_a1/
%G ru
%F MM_2004_16_5_a1

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

We consider the “authority-society” model by A. P. Mikhailov. We introduce the generalized approach which supposes the existence of two stable authority profiles. The first profile is related to the hierarchy having a large amount of powers, the second one – a small amount of powers. We have shown that depending on the initial conditions and system parameters the authority profile at large values of time appears to be close to either one of these profiles or the so-called contrast profile.

[1] Mikhailov A. P., “Matematicheskoe modelirovanie vlasti v ierarkhicheskikh strukturakh”, Matem. modelirovanie, 6:6 (1994), 108–138

[2] Samarskii A. A., Mikhailov A. P., Matematicheskoe modelirovanie, Nauka. Fizmatlit, M., 2001 | Zbl

[3] Mikhailov A. P., “Mathematical modeling of power distribution in state hierarchical structures interacting with civil society”, Proc. of 14 IMACS World Congress (Atlanta, USA, 1994), 2, 828–830

[4] Klokov Yu. A., Mikhailov A. P., “Ob odnoi zadache Neimana dlya integro-differentsialnogo uravneniya”, Differentsialnye uravneniya, 32:8 (1996), 1110–1113 | MR | Zbl

[5] Mikhailov A. P., Yukhno L. F., “Prosteishaya model ustanovleniya ravnovesiya mezhdu dvumya vetvyami vlasti”, Matematicheskoe modelirovanie, 13:1 (2001), 65–76 | MR | Zbl

[6] Dmitriev M. G., Petrov A. P., “Analiz modeli “vlast-obschestvo” dlya sluchaya dvukh ustoichivykh raspredelenii vlasti”, Matematicheskie metody i prilozheniya, Trudy devyatykh matematicheskikh chtenii, MGSU, M., 2002, 150–154

[7] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vysshaya shkola, M., 1990, 208 pp. | MR

[8] Butuzov V. F., Vasileva A. B., “Ob asimptoticheskoi teorii prostranstvennykh kontrastnykh struktur”, Zh. vychisl. matem. i matematicheskoi fiziki, 28:3 (1988), 346–361 | MR | Zbl

[9] Vasileva A. B., “Ob ustoichivosti kontrastnykh struktur”, Matem. modelirovanie, Z:4 (1991), 114–123 | MR

[10] Vasileva A. B., Nikitin A. G., Petrov A. P., “Asimptoticheskii metod issledovaniya kontrastnykh struktur i ego prilozhenie k teorii gidromagnitnogo dinamo”, Matem. modelirovanie, 7:2 (1995), 61–71 | MR

[11] Vasileva A. B., Petrov A. P., Plotnikov A. A., “K teorii kontrastnykh struktur peremennogo tipa”, Zh. vychisl. matem. i matem. fiz., 38:9 (1998), 1534–1543 | MR

[12] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya ustoichivykh reshenii s vnutrennimi sloyami”, Matem. sbornik, 192:5 (2001), 13–52 | MR

[13] Moss D., Petrov A., Sokoloff D., “The motion of magnetic fronts in spiral galaxies”, Geophysical and Astrophysical fluid Dynamics, 92, 129–149 | DOI | MR