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Avtomatika i Telemekhanika, 2017, Issue 4, Pages 63–77 (Mi at14770)  
Nonlinear Systems

The parameter functionalization method for the problem of saddle-node bifurcations in dynamical systems

M. G. Yumagulov, E. S. Imangulova

Bashkiria State University, Ufa, Russia
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Abstract: We propose new sufficient conditions for saddle-node bifurcations in one- and twoparametric dynamical systems obtained with the parameter functionalization method, derive asymptotic formulas for the resulting solutions, and analyze their stability. As an application, we consider the synchronization problem for periodic oscillations of an autonomous Van der Pol generator under an external harmonic influence.
Keywords: dynamical system, saddle-node bifurcation, periodic oscillations, synchronization, stability, parameter functionalization.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00567-а
This work was partially supported by the Russian Foundation for Basic Research, project no. 12-01-00567-a.
Presented by the member of Editorial Board: A. M. Krasnosel'skii

Received: 10.12.2014
English version:
Automation and Remote Control, 2017, Volume 78, Issue 4, Pages 630–642
DOI: https://doi.org/10.1134/S0005117917040051
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. G. Yumagulov, E. S. Imangulova, “The parameter functionalization method for the problem of saddle-node bifurcations in dynamical systems”, Avtomat. i Telemekh., 2017, no. 4, 63–77; Autom. Remote Control, 78:4 (2017), 630–642
Citation in format AMSBIB
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