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Ufa Mathematical Journal, 2014, Volume 6, Issue 2, Pages 102–110
DOI: https://doi.org/10.13108/2014-6-2-102 (Mi ufa248) 		 
Study of main scenarios of bifurcation for functional differential time-delay equations

M. G. Yumagulova, D. A. Yakshibaevab

a Bashkir State University, Ufa, Russia
b Sibai Institute (Branch of Bashkir State University), Sibai, Russia
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DOI: https://doi.org/10.13108/2014-6-2-102
Abstract: In the paper, we study the main bifurcation scenarios for functional differential time delay equations with periodic right side and for nonlinear autonomous equations with aftereffect. The main tool is the operator method for studying multi-parameter bifurcation leading us to new sufficient bifurcation conditions and allowing us to obtain the approximate formulae for appearing solutions. As applications, we consider the problems on bifurcation points for the modifications of Duffing equation and Hutchinson–Wright equation.
Keywords: functional differential equations, time-delay system, dynamical systems, bifurcation, operator method, functionalization parameter, asymptotic formula.
Received: 25.11.2013
Russian version:
Ufimskii Matematicheskii Zhurnal, 2014, Volume 6, Issue 2, Pages 104–112
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 34C23, 34K05,34K13, 34K18
Language: English
Original paper language: Russian
Citation: M. G. Yumagulov, D. A. Yakshibaeva, “Study of main scenarios of bifurcation for functional differential time-delay equations”, Ufa Math. J., 6:2 (2014), 102–110
Citation in format AMSBIB
\Bibitem{YumYak14}
\by M.~G.~Yumagulov, D.~A.~Yakshibaeva
\paper Study of main scenarios of bifurcation for functional differential time-delay equations
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 102--110
\mathnet{http://mi.mathnet.ru//eng/ufa248}
\crossref{https://doi.org/10.13108/2014-6-2-102}
\elib{https://elibrary.ru/item.asp?id=21596978}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928187141}
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    Russian version PDF:142
    English version PDF:13
    References:39
     
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