Geodesic
Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 29-43.

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

We consider a system of ordinary differential equations, which describes a model of the pedagogical impact on a group of students. The impact is expressed as the sum of a constant and a control parameter. We find equilibrium states of the system and determine the types of their bifurcations that arise when the control parameter changes. Also, we obtain coefficient conditions for the emergence of stable equilibrium states and the corresponding bifurcation values of the parameter.
Keywords: differential equation, equilibrium state, control parameter, periodic solution.
Mots-clés : bifurcation 
@article{INTO_2022_216_a2,
     author = {S. A. Belman and E. Yu. Liskina},
     title = {Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {29--43},
     publisher = {mathdoc},
     volume = {216},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_216_a2/}
}
TY  - JOUR
AU  - S. A. Belman
AU  - E. Yu. Liskina
TI  - Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 29
EP  - 43
VL  - 216
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_216_a2/
LA  - ru
ID  - INTO_2022_216_a2
ER  - 
%0 Journal Article
%A S. A. Belman
%A E. Yu. Liskina
%T Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 29-43
%V 216
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_216_a2/
%G ru
%F INTO_2022_216_a2
S. A. Belman; E. Yu. Liskina. Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 29-43. http://geodesic.mathdoc.fr/item/INTO_2022_216_a2/

[1] Atryakhin V. A., Shamanaev P. A., “Postroenie matematicheskoi modeli dinamiki potoka pretendentov na postuplenie v aspiranturu s ispolzovaniem sistemy differentsialnykh uravnenii s zapazdyvaniem”, Zh. Srednevolzh. mat. o-va., 13:4 (2011), 35–39 | MR

[2] Atryakhin V. A., Shamanaev P. A., “Modelirovanie dinamiki kadrov s ispolzovaniem differentsialnykh uravnenii s otklonyayuschimsya argumentom”, Zh. Srednevolzh. mat. o-va., 14:1 (2012), 35–39

[3] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1991

[4] Belman S. A., Bykova A. A., “Issledovanie dinamicheskoi modeli pedagogicheskikh resursov”, Vestn. RAEN., 19:2 (2019), 36–38

[5] Belman S. A., Liskina E. Yu., “O regulirovanii pedagogicheskogo vozdeistviya v dinamicheskoi modeli studencheskoi gruppy, imeyuschei otritsatelnogo neformalnogo lidera”, Differ. uravn. mat. model., 2021, no. 2, 10–19

[6] Malinetskii G. G., Potapov A. B., Sovremennye problemy nelineinoi dinamiki, Editorial URSS, M., 2000

[7] Matematicheskie modeli sotsialnykh sistem, Omsk. gos. un-t, Omsk, 2000

[8] Matematicheskoe modelirovanie sotsialnykh protsessov / Sb. nauch. trudov, IPM im. M. V. Keldysha, M., 2017. — No 19

[9] Mikhailov A. P., Petrov A. P., “Povedencheskie gipotezy i matematicheskoe modelirovanie v gumanitarnykh naukakh”, Mat. model., 23:6 (2011), 18–32 | MR

[10] Mikhailov A. P., Proncheva O. G., “Destabiliziruyuschee vozdeistvie na sotsium v modelyakh informatsionnogo protivoborstva”, Matematicheskoe modelirovanie sotsialnykh protsessov, IPM im. M. V. Keldysha, M., 2017. — 19, 51–57

[11] Modelirovanie sotsialno-pedagogicheskikh sistem / Mat. region. nauch.-prakt. konf, Perm. gos. ped. un-t, Perm, 2004

[12] Yadrovskaya M. V., “Modelirovanie pedagogicheskogo vzaimodeistviya”, Obrazovatelnye tekhnologii i obschestvo., 2009, no. 3, 354–362