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

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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/}
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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/