Classes of linear approximations providing different stability or instability types of differential systems

DOI10.3103/s0027132223040083OpenAlexW4388377391MaRDI QIDQ6154995

I. N. Sergeev

Publication date: 16 February 2024

Published in: Moscow University Mathematics Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s0027132223040083

zbMATH Keywords

nonlinear systemLyapunov stabilitylinear approximationdifferential systemPerron stabilityupper-limit stabilitystability in first approximation

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Linear ordinary differential equations and systems (34A30) Nonautonomous smooth dynamical systems (37C60)

Cites Work

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• Studying the Perron and Lyapunov stability properties by the first approximation
• Dependence and independence of the Perron and Lyapunov stability properties on the system phase domain
• Definition and some properties of Perron stability
• Perron stability and its study at the first approximation
• Examples of differential systems with contrasting combinations of Lyapunov, Perron, and upper-limit properties
• Lyapunov, Perron and upper-limit stability properties of autonomous differential systems