Localizing sets and trajectory behavior
- Authors: Kanatnikov A.N.1,2, Krishchenko A.P.1,2
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Affiliations:
- Bauman Moscow State Technical University
- Institute for Systems Analysis, Federal Research Center “Computer Science and Control,”
- Issue: Vol 94, No 2 (2016)
- Pages: 506-509
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224216
- DOI: https://doi.org/10.1134/S1064562416050070
- ID: 224216
Cite item
Abstract
The problem is considered of finding domains in the phase space in which the trajectories of a system have a fairly simple behavior determined by a typical scenario. The problem is solved by applying the method of localization of compact invariant sets of the system. It is proved that localizing sets separate simple and complex dynamics of nonlinear systems, namely, in the complement of any localizing set, the trajectory behavior of a system admits a standard description in the form of several scenarios, while, in localizing sets and their intersections, the trajectory behavior of the system can be very complex. Specifically, it is shown that the α- and ω-limit sets of any trajectory are contained in localizing sets.
About the authors
A. N. Kanatnikov
Bauman Moscow State Technical University; Institute for Systems Analysis, Federal Research Center “Computer Science and Control,”
Author for correspondence.
Email: skipper@bmstu.ru
Russian Federation, Vtoraya Baumanskaya ul. 5, Moscow, 105005; pr. 60-letiya Oktyabrya 9, Moscow, 117312
A. P. Krishchenko
Bauman Moscow State Technical University; Institute for Systems Analysis, Federal Research Center “Computer Science and Control,”
Email: skipper@bmstu.ru
Russian Federation, Vtoraya Baumanskaya ul. 5, Moscow, 105005; pr. 60-letiya Oktyabrya 9, Moscow, 117312