M. G. Yumagulov, D. A. Yakshibaeva, “Operator method for the study of small oscillations in systems with aftereffect”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, Issue 9/2(110),Pages <nobr>37

Mathematics

Operator method for the study of small oscillations in systems with aftereffect

M. G. Yumagulov^a, D. A. Yakshibaeva^b

^a The Dept. of Differential Equations, Bashkir State University, Ufa, 450008, Russian Federation
^b The Dept. of Applied Mathematics and Information Technology, Sibai Institute (branch) of Bashkir State University, Sibai, 453837, Russian Federation

Abstract: This paper proposes operator method for the study of effect of appearence of small oscillations in systems with aftereffect.The method leads to new sufficient features of Andronov–Hopf bifurkation and allows to obtain approximate formulas for emerging decisions. As an application, we consider the problem of bifurcation points of Hutchinson–Wright equation.

Keywords: bifurcation, dynamic systems, time-delay systems, operator equations, functionalization of parameter, asymptotic formulae.

UDC: 517.938

Received: 13.05.2013
Revised: 13.05.2013