Geodesic
Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System
Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 895-904.

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

We consider the problem of the possibility randomly of choosing the initial value for a perturbed solution of a given differential system so that it remained close to the initial zero solution. In this regard, we introduce completely new concepts and study (as applied to different classes of systems) the measure of stability and the measure of instability of various types: Lyapunov, Perron, or upper-limit.
Keywords: differential system, Lyapunov stability, Perron stability, upper-limit stability, measure of stability. 
@article{MZM_2023_113_6_a8,
     author = {I. N. Sergeev},
     title = {Definition and {Properties} of {Measures} of {Stability} and {Instability} of {Zero} {Solution} of a {Differential} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {895--904},
     publisher = {mathdoc},
     volume = {113},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a8/}
}
TY  - JOUR
AU  - I. N. Sergeev
TI  - Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System
JO  - Matematičeskie zametki
PY  - 2023
SP  - 895
EP  - 904
VL  - 113
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a8/
LA  - ru
ID  - MZM_2023_113_6_a8
ER  - 
%0 Journal Article
%A I. N. Sergeev
%T Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System
%J Matematičeskie zametki
%D 2023
%P 895-904
%V 113
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a8/
%G ru
%F MZM_2023_113_6_a8
I. N. Sergeev. Definition and Properties of Measures of Stability and Instability of Zero Solution of a Differential System. Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 895-904. http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a8/

[1] K. Ito, G. Makkin, Diffuzionnye protsessy i ikh traektorii, Mir, M., 1965 | MR

[2] R. Z. Khasminskii, Ustoichivost sistem differentsialnykh uravnenii pri sluchainykh vozmuscheniyakh ikh parametrov, Nauka, M., 1969 | MR

[3] A. D. Venttsel, M. I. Freidlin, Fluktuatsii v dinamicheskikh sistemakh pod deistviem malykh sluchainykh vozmuschenii, Nauka, M., 1979 | MR

[4] A. M. Lyapunov, Obschaya zadacha ob ustoichivosti dvizheniya, GITTL, M.–L., 1950 | MR

[5] B. F. Bylov, R. E. Vinograd, D. M. Grobman, V. V. Nemytskii, Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR

[6] B. P. Demidovich, Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

[7] I. N. Sergeev, “Opredelenie i nekotorye svoistva ustoichivosti po Perronu”, Differents. uravneniya, 55:5 (2019), 636–646 | DOI

[8] O. Perron, “Die Ordnungszahlen linearer Differentialgleichungssysteme”, Math. Z., 31:1 (1930), 748–766 | DOI | MR

[9] N. A. Izobov, Vvedenie v teoriyu pokazatelei Lyapunova, BGU, Minsk, 2006

[10] I. N. Sergeev, “Lyapunovskie, perronovskie i verkhnepredelnye svoistva ustoichivosti avtonomnykh differentsialnykh sistem”, Izv. In-ta matem. i inf. Udmurtskogo gos. un-ta, 56:2 (2020), 63–78 | MR

[11] I. N. Sergeev, “Massivnye i pochti massivnye svoistva ustoichivosti i neustoichivosti”, Tezisy dokladov Mezhdunarodnoi konferentsii “Differentsialnye uravneniya i smezhnye voprosy”, Izd-vo MGU, M., 2021, 317–319

[12] I. N. Sergeev, “Opredelenie ustoichivosti po Perronu i ee svyaz s ustoichivostyu po Lyapunovu”, Differents. uravneniya, 54:6 (2018), 855–856

[13] I. N. Sergeev, “Opredelenie verkhnepredelnoi ustoichivosti i ee svyaz s ustoichivostyu po Lyapunovu i ustoichivostyu po Perronu”, Differents. uravneniya, 56:11 (2020), 1556–1557

[14] I. N. Sergeev, “Massivnye i pochti massivnye svoistva ustoichivosti i neustoichivosti differentsialnykh sistem”, Differents. uravneniya, 57:11 (2021), 1576–1578

[15] A. F. Filippov, Vvedenie v teoriyu differentsialnykh uravnenii, Editorial URSS, M., 2004 | MR