Global Asymptotic Stability in a Non-autonomous Difference Equation

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Abstract

Non-autonomous first order difference equation of the form (Formula Presented) is considered where (Formula Presented) is a continuous function satisfying the negative feedback assumption (Formula Presented) and (Formula Presented) is a non-negative sequence. Sufficient conditions for the global asymptotic stability of the zero solution are derived in terms of the attractivity of the fixed point x*=0 under the iterations of distinct maps of the family of one-dimensional maps (Formula Presented) The principal motivation for consideration of the difference equation and the corresponding family of interval maps comes from a problem of asymptotic behavior in differential equations with piece-wise constant argument (DEPCA).

Original languageEnglish (US)
Title of host publicationDifference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018
EditorsMartin Bohner, Stefan Siegmund, Roman Šimon Hilscher, Petr Stehlík
PublisherSpringer
Pages231-250
Number of pages20
ISBN (Print)9783030355012
DOIs
StatePublished - Jan 1 2020
Event24th International Conference on Difference Equations and Applications, ICDEA 2018 - Dresden, Germany
Duration: May 21 2018May 25 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume312
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference24th International Conference on Difference Equations and Applications, ICDEA 2018
CountryGermany
CityDresden
Period5/21/185/25/18

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Ivanov, A. F. (2020). Global Asymptotic Stability in a Non-autonomous Difference Equation. In M. Bohner, S. Siegmund, R. Šimon Hilscher, & P. Stehlík (Eds.), Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018 (pp. 231-250). (Springer Proceedings in Mathematics and Statistics; Vol. 312). Springer. https://doi.org/10.1007/978-3-030-35502-9_10