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ITERATIVE SEQUENCES OF THE LOCALIZATION METHOD
- Authors: Krishchenko A.P1
-
Affiliations:
- Bauman Moscow State Technical University
- Issue: Vol 60, No 11 (2024)
- Pages: 1460-1470
- Section: ORDINARY DIFFERENTIAL EQUATIONS
- URL: https://rjmseer.com/0374-0641/article/view/649586
- DOI: https://doi.org/10.31857/S0374064124110037
- EDN: https://elibrary.ru/JELHZZ
- ID: 649586
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Abstract
The conditions of positive invariance and compactness of localizing sets and extended localizing sets are proved. The necessary condition for the existence of an attractor in the system is obtained. The concept of an iterative sequence of extended localizing sets is introduced and a condition is obtained under which its elements are positively invariant compact sets and give an estimate of the attraction set. Using the obtained results the behavior of the trajectories of a three-dimensional system for acceptable values of its parameters is investigated. The conditions of global stability of one of its equilibrium point are found and the set of attraction of another equilibrium point is indicated.
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