Methods for Studying the Stability of Linear Periodic Systems Depending on a Small Parameter

In this paper, we consider systems of linear differential equations with periodic coefficients depending on a small parameter. We propose new approaches to the problem of constructing a monodromy matrix that lead to new effective formulas for calculating multipliers of the system studies. We present...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 258; no. 1; pp. 115 - 127
Main Authors Yumagulov, M. G., Ibragimova, L. S., Belova, A. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2021
Springer
Springer Nature B.V
Subjects
Analysis
Differential equations
Dynamic stability
Linear operators
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Operators (mathematics)
Parameters
Perturbation theory
Stability analysis
differential equation
monodromy matrix
multiplier
34D20
Hamiltonian system
periodic system
stability
small parameter
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Summary:In this paper, we consider systems of linear differential equations with periodic coefficients depending on a small parameter. We propose new approaches to the problem of constructing a monodromy matrix that lead to new effective formulas for calculating multipliers of the system studies. We present a number of applications in problems of the perturbation theory of linear operators, in the analysis of stability of linear differential equations with periodic coefficients, in the problem of constructing the stability domains of linear dynamical systems, etc.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05540-x