On the dynamics of certain higher-order scalar difference equation: asymptotics, oscillation, stability | Zendy

П. Н. Нестеров | Zendy

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On the dynamics of certain higher-order scalar difference equation: asymptotics, oscillation, stability

Author(s) -

П. Н. Нестеров

Publication year - 2020

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1912-89

Subject(s) - mathematics , oscillation (cell signaling) , dynamics (music) , scalar (mathematics) , stability (learning theory) , mathematical analysis , order (exchange) , geometry , physics , genetics , finance , machine learning , computer science , acoustics , economics , biology

We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation ∆y(n) = −g(n)y(n − k) . We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as n → ∞ . Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.

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