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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 2, Pages 104–112 (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

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.

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English version:
Ufa Mathematical Journal, 2014, 6:2, 102–110 (PDF, 336 kB); https://doi.org/10.13108/2014-6-2-102

UDC: 517.956
MSC: 34C23, 34K05,34K13, 34K18
Received: 25.11.2013

Citation: M. G. Yumagulov, D. A. Yakshibaeva, “Study of main scenarios of bifurcation for functional differential time-delay equations”, Ufimsk. Mat. Zh., 6:2 (2014), 104–112; Ufa Math. J., 6:2 (2014), 102–110

Citation in format AMSBIB
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\by M.~G.~Yumagulov, D.~A.~Yakshibaeva
\paper Study of main scenarios of bifurcation for functional differential time-delay equations
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 2
\pages 104--112
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\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 2
\pages 102--110
\crossref{https://doi.org/10.13108/2014-6-2-102}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928187141}


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