Publication 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

conference paper

Language

en

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

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

Edition number

312

Pages from

355

Pages to

364

Pages count

10

Documents

BibTex


@inproceedings{BUT162607,
  author="Petr {Tomášek}",
  title="Stability and Instability Regions for a Three Term Difference Equation",
  annote="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.",
  address="Springer",
  booktitle="Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018.",
  chapter="162607",
  doi="10.1007/978-3-030-35502-9_16",
  edition="Springer Proceedings in Mathematics & Statistics",
  howpublished="online",
  institution="Springer",
  year="2020",
  month="february",
  pages="355--364",
  publisher="Springer",
  type="conference paper"
}