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Avtomatika i Telemekhanika, 2020, Issue 1, Pages 34–51
DOI: https://doi.org/10.31857/S0005231020010031 (Mi at15417) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Nonlinear Systems

Approximate formulas and algorithms for constructing central manifolds of dynamic systems

M. G. Yumagulova, M. F. Fazlytdinovb

a Bashkir State University, Ufa, Russia
b JSC Gazpromneft Science and Research Center, St. Petersburg, Russia
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DOI: https://doi.org/10.31857/S0005231020010031
Abstract: New approaches to obtain approximations of the second and higher orders for the central manifolds of non-hyperbolic equilibria of continuous- and discrete-time dynamic systems are proposed. The formulas derived below lead to new practical algorithms for constructing central manifolds. The formulas and algorithms are general in the sense that they can be used to construct central manifolds in terms of the original equations and are applicable to the cases in which the linearization matrix has an arbitrary order of degeneracy.
Keywords: dynamic systems, equilibrium, central manifold, bifurcation, approximation, approximate formulas, algorithms.
Presented by the member of Editorial Board: A. N. Sobolevski

Received: 31.12.2018
Revised: 04.05.2019
Accepted: 18.07.2019
English version:
Automation and Remote Control, 2020, Volume 81, Issue 1, Pages 27–40
DOI: https://doi.org/10.1134/S0005117920010038
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. G. Yumagulov, M. F. Fazlytdinov, “Approximate formulas and algorithms for constructing central manifolds of dynamic systems”, Avtomat. i Telemekh., 2020, no. 1, 34–51; Autom. Remote Control, 81:1 (2020), 27–40
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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