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Avtomatika i Telemekhanika, 2017, Issue 10, Pages 74–89 (Mi at14635)  
This article is cited in 1 scientific paper (total in 1 paper)

Nonlinear Systems

A study of the boundaries of stability regions in two-parameter dynamical systems

M. G. Yumagulova, I. Zh. Mustafinaa, L. S. Ibragimovab

a Bashkir State University, Ufa, Russia
b Bashkir State Agrarian University, Ufa, Russia
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Abstract: We consider dynamical systems defined by autonomous and periodic differential equations that depend on two scalar parameters. We study the problems of constructing boundaries of stability regions for equilibrium points in the plane of parameters. We identify conditions under which a point on the boundary of a stability region has one or more smooth boundary curves coming through it. We show schemes to find the basic scenarios of bifurcations when parameters transition over the boundaries of stability regions. We distinguish types of boundaries (dangerous or safe). The main formulas have been obtained in the terms of original equations and do not require to pass to normal forms and using theorems on a central manifold.
Keywords: dynamical systems, Hamiltonian systems, equilibrium point, stability, boundary of a stability region, dangerous and safe boundaries, bifurcations.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-20820
This work was supported in part by the Russian Foundation for Basic Research, project no. 15-01-20820.
Presented by the member of Editorial Board: A. M. Krasnosel'skii

Received: 22.12.2016
English version:
Automation and Remote Control, 2017, Volume 78, Issue 10, Pages 1790–1802
DOI: https://doi.org/10.1134/S0005117917100046
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. G. Yumagulov, I. Zh. Mustafina, L. S. Ibragimova, “A study of the boundaries of stability regions in two-parameter dynamical systems”, Avtomat. i Telemekh., 2017, no. 10, 74–89; Autom. Remote Control, 78:10 (2017), 1790–1802
Citation in format AMSBIB
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\paper A study of the boundaries of stability regions in two-parameter dynamical systems
\jour Avtomat. i Telemekh.
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\issue 10
\pages 74--89
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\jour Autom. Remote Control
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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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