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JOURNALS // Ufimskii Matematicheskii Zhurnal // Archive

Ufimsk. Mat. Zh., 2010 Volume 2, Issue 4, Pages 3–26 (Mi ufa68)

This article is cited in 18 papers

An operator method for approximate investigation of a regular bifurcation in multiparameter dynamical systems

A. A. Vyshinskiya, L. S. Ibragimovab, S. A. Murtazinaa, M. G. Yumagulovc

a Sibai Institute (Branch) of Bashkir State University, Sibai, Russia
b Bashkir State Agricultural University, Ufa, Russia
c Bashkir State University, Ufa, Russia

Abstract: A new operator method for investigating a large class of bifurcation problems with multidimensional degenerations is considered. The method makes it possible to detect bifurcation parameter values; it leads to an iteration procedure and asymptotic formulae for approximate investigation of problems depending on many parameters. Applications to the theory of dynamical systems are discussed, e.g. in problems on bifurcation of fixed points, forced oscillations and self-oscillations.

Keywords: bifurcation, dynamic systems, the operational equations, parameter functionalization, asymptotic formulas.

UDC: 517.91

Received: 05.04.2010



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