Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation

The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding character...

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Bibliographic Details
Published inMathematical Notes Vol. 115; no. 3-4; pp. 599 - 606
Main Author Sergeev, I. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2024
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Approximation
Differential equations
Mathematics
Mathematics and Statistics
Rotation
complete wandering
ball index
differential system
complete oscillation
complete rotation
first approximation study
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Summary:The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434624030313