About construction stability regions of equilibrium points of differential equations

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Doklady Bashkirskogo Universiteta. 2016. Volume 1. No. 1. pp. 14-21.

Authors

Yumagulov M. G.*
Bashkir State University
450074, Russia, Ufa, Z. Validy str., 32
Ibragimova L. S.
Bashkir State Agrarian University
450001, Russia, Ufa, 50- anniversary of October str., 34
Mustafina I. G.
Bashkir State University
450074, Russia, Ufa, Z. Validy str., 32

Abstract

The paper proposes a new general approach that allows to study the problem of constructing stability regions of nonlinear differential equations. The approach is based on a modification of the method of M. Rozo for the study of stability of linear systems with periodic coefficients depending on a small parameter and asymptotic formulas of the perturbation theory of linear operators. The approximate formulas describing the boundary of the stability regions.

Keywords

  • differential equation
  • equilibrium points
  • periodic solutions
  • stability
  • stability region
  • small parameter
  • asymptotic formula
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