Publication detail

General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions

DIBLÍK, J. HALFAROVÁ, H.

Original Title

General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions

English Title

General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions

Type

journal article in Web of Science

Language

en

Original Abstract

Planar linear discrete systems with constant coefficients and delays are considered. It is assumed that the considered system is weakly delayed. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

English abstract

Planar linear discrete systems with constant coefficients and delays are considered. It is assumed that the considered system is weakly delayed. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

Keywords

Discrete equation, weakly delayd systems, explicit solution, dimension of the solutions space.

RIV year

2014

Released

29.04.2014

Publisher

Hindawi

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Year of study

2013

Number

1

State

US

Pages from

1

Pages to

37

Pages count

37

URL

Full text in the Digital Library

Documents

BibTex


@article{BUT107603,
  author="Josef {Diblík} and Hana {Halfarová}",
  title="General explicit solution of planar weakly delayed linear discrete systems and pasting its solutions",
  annote="Planar linear discrete systems with constant coefficients and delays are considered. It is assumed that the considered system is weakly delayed. The characteristic equations of such systems are identical with those for the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.",
  address="Hindawi",
  chapter="107603",
  doi="10.1155/2014/627295",
  institution="Hindawi",
  number="1",
  volume="2013",
  year="2014",
  month="april",
  pages="1--37",
  publisher="Hindawi",
  type="journal article in Web of Science"
}