On the behaviour of the solutions of a k -order cyclic-type system of max difference equations

Gesthimani Stefanidou; Garyfalos Papaschinopoulos

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 297-325
  • ISSN: 0011-4642

Abstract

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We investigate the behaviour of the solutions of a k -dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when k is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where k = 2 and k = 4 .

How to cite

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Stefanidou, Gesthimani, and Papaschinopoulos, Garyfalos. "On the behaviour of the solutions of a $k$-order cyclic-type system of max difference equations." Czechoslovak Mathematical Journal (2025): 297-325. <http://eudml.org/doc/299912>.

@article{Stefanidou2025,
abstract = {We investigate the behaviour of the solutions of a $k$-dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where $k=2$ and $k=4$.},
author = {Stefanidou, Gesthimani, Papaschinopoulos, Garyfalos},
journal = {Czechoslovak Mathematical Journal},
keywords = {difference equation with maximum; cyclic system; equilibrium; asymptotic behavior},
language = {eng},
number = {1},
pages = {297-325},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the behaviour of the solutions of a $k$-order cyclic-type system of max difference equations},
url = {http://eudml.org/doc/299912},
year = {2025},
}

TY - JOUR
AU - Stefanidou, Gesthimani
AU - Papaschinopoulos, Garyfalos
TI - On the behaviour of the solutions of a $k$-order cyclic-type system of max difference equations
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 297
EP - 325
AB - We investigate the behaviour of the solutions of a $k$-dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where $k=2$ and $k=4$.
LA - eng
KW - difference equation with maximum; cyclic system; equilibrium; asymptotic behavior
UR - http://eudml.org/doc/299912
ER -

References

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