Open AccessLyapunov, Perron and upper-limit stability properties of autonomous differential systems
Author(s) -
И. Н. Сергеев
Publication year - 2020
Language(s) - English
DOI - 10.35634/2226-3594-2020-56-06
Subject(s) - mathematics , lyapunov function , limit (mathematics) , exponential stability , stability (learning theory) , instability , singular point of a curve , lyapunov exponent , differential (mechanical device) , mathematical analysis , limit cycle , control theory (sociology) , nonlinear system , computer science , physics , control (management) , quantum mechanics , machine learning , artificial intelligence , mechanics , thermodynamics
For a singular point of an autonomous differential system, the natural concepts of its Perron and upper-limit stability are defined, reminiscent of Lyapunov stability. Numerous varieties of them are introduced: from asymptotic and global stability to complete and total instability. Their logical connections with each other are investigated: cases of their coincidence are revealed and examples of their possible differences are given. The invariance of most of these properties with respect to the narrowing of the phase region of the system is established.