Behavior of Trajectories in Localizing Sets
- Authors: 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 97, No 3 (2018)
- Pages: 243-246
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225504
- DOI: https://doi.org/10.1134/S1064562418030146
- ID: 225504
Cite item
Abstract
It is well known that simple and complex dynamics of a nonlinear system are separated by a localizing set that contains all compact invariant sets and corresponds to a function in the phase space of the system. This separation means that, in the complement of the localizing set, the trajectory behavior of the system admits a standard description in the form of several variants, while, in the localizing set, the trajectory behavior of the system can be very complex, for example, chaotic. Domains in the localizing set with a similar standard behavior are indicated, and an external estimate of the domain with complex dynamics is sequentially refined. Two examples are considered.
About the authors
A. P. Krishchenko
Bauman Moscow State Technical University; Institute for Systems Analysis, Federal Research Center “Computer Science and Control,”
Author for correspondence.
Email: apkri@bmstu.ru
Russian Federation, Moscow, 105005; Moscow, 117312