Article
Ufa Mathematical Journal
Volume 8, Number 3, pp. 58-78
The asymptotic formulae in the problem on constructing hyperbolicity and stability regions of dynamical systems
Fanina I.G., Ibragimova L.S., Yumagulov M.G.
DOI:10.13108/2016-8-3-58
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Article on MathNetAbstact
The paper proposes a new general
method allowing one to study the problem on constructing
hyperbolicity and stability regions for nonlinear dynamical
systems. The method is based on a modification of M. Rozo method for
studying the stability of linear systems with periodic
coefficients depending on a small parameter and on the asymptotic
formulae in the perturbation theory of linear operators. We obtain approximate formulae describing the boundary of hyperbolicity and stability regions. As an example, we provide the scheme for constructing the stability regions for Mathieu equation.