Publication detail

Stability and Instability Regions for a Three Term Difference Equation

TOMÁŠEK, P.

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 in English

Instability degree; linear difference equation; stability

Released

11.02.2020

Publisher

Springer

Location

Cham

ISBN

978-3-030-35501-2

ISSN

2194-1009

Book

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

Volume

312

Edition number

312

Pages from–to

355–364

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",
  volume="312",
  month="February",
  pages="355--364",
  publisher="Springer",
  address="Cham",
  isbn="978-3-030-35501-2",
  issn="2194-1009"
}