Publication result detail

Stability and Instability Regions for a Three Term Difference Equation

TOMÁŠEK, P.

Original Title

Stability and Instability Regions for a Three Term Difference Equation

English Title

Stability and Instability Regions for a Three Term Difference Equation

Type

Paper in proceedings (conference paper)

Original Abstract

The paper discusses stability and instability properties of difference equation y(n+1)+ay(n-l+1)+by(n-l)=0 with real parameters a, b. Beside known results about its asymptotic stability conditions a deeper analysis of instability properties is introduced. An instability degree of difference equation’s solution is introduced in analogy with theory of differential equations. Instability regions of a fixed degree are introduced and described in the paper. It is shown that dislocation of instability regions of various degrees obeys some rules and qualitatively depends on parity of difference equation’s order.

English abstract

The paper discusses stability and instability properties of difference equation y(n+1)+ay(n-l+1)+by(n-l)=0 with real parameters a, b. Beside known results about its asymptotic stability conditions a deeper analysis of instability properties is introduced. An instability degree of difference equation’s solution is introduced in analogy with theory of differential equations. Instability regions of a fixed degree are introduced and described in the paper. It is shown that dislocation of instability regions of various degrees obeys some rules and qualitatively depends on parity of difference equation’s order.

Keywords

Instability degree; linear difference equation; stability

Key words in English

Instability degree; linear difference equation; stability

Authors

TOMÁŠEK, P.

RIV year

2021

Released

11.02.2020

Publisher

Springer

Location

Cham

ISBN

978-3-030-35501-2

Book

Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018.

Edition

Springer Proceedings in Mathematics & Statistics

ISBN

2194-1009

Periodical

Springer Proceedings in Mathematics & Statistics

Volume

312

State

Federal Republic of Germany

Pages from

355

Pages to

364

Pages count

10

BibTex

@inproceedings{BUT162607,
  author="Petr {Tomášek}",
  title="Stability and Instability Regions for a Three Term Difference Equation",
  booktitle="Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018.",
  year="2020",
  series="Springer Proceedings in Mathematics & Statistics",
  journal="Springer Proceedings in Mathematics & Statistics",
  volume="312",
  number="312",
  pages="355--364",
  publisher="Springer",
  address="Cham",
  doi="10.1007/978-3-030-35502-9\{_}16",
  isbn="978-3-030-35501-2",
  issn="2194-1009"
}