Global behavior of P-dimensional difference equations system

Amira Khelifa; Yacine Halim; Amira Khelifa; Yacine Halim

doi:10.3934/era.2021029

Electronic Research Archive

2021, Volume 29, Issue 5: 3121-3139. doi: 10.3934/era.2021029

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Global behavior of P-dimensional difference equations system

Amira Khelifa ^{1
,},
Yacine Halim ^{2
,
,}

1.
Department of Mathematics and LMAM laboratory, Mohamed Seddik Ben Yahia University, BP 98 Ouled Aissa 18000, Jijel, Algeria
2.
Department of Mathematics and Computer Sciences, Abdelhafid Boussouf University Center, RP 26 Mila 43000, Mila, Algeria

Received: 01 January 2021 Revised: 01 March 2021 Published: 15 April 2021
Primary: 39A10; Secondary: 40A05

The global asymptotic stability of the unique positive equilibrium point and the rate of convergence of positive solutions of the system of two recursive sequences has been studied recently. Here we generalize this study to the system of $ p $ recursive sequences $x_{n+1}^{(j)}=A+\left(x_{n-m}^{(j+1) mod (p)} \;\;/ x_{n}^{(j+1) mod (p)}\;\;\;\right) $, $ n = 0,1,\ldots, $ $ m,p\in \mathbb{N} $, where $ A\in(0,+\infty) $, $ x_{-i}^{(j)} $ are arbitrary positive numbers for $ i = 1,2,\ldots,m $ and $ j = 1,2,\ldots,p. $ We also give some numerical examples to demonstrate the effectiveness of the results obtained.
- System of difference equations,
- global asymptotic stability,
- boundedness,
- rate of convergence
Citation: Amira Khelifa, Yacine Halim. Global behavior of P-dimensional difference equations system[J]. Electronic Research Archive, 2021, 29(5): 3121-3139. doi: 10.3934/era.2021029

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Abstract

The global asymptotic stability of the unique positive equilibrium point and the rate of convergence of positive solutions of the system of two recursive sequences has been studied recently. Here we generalize this study to the system of $ p $ recursive sequences $x_{n+1}^{(j)}=A+\left(x_{n-m}^{(j+1) mod (p)} \;\;/ x_{n}^{(j+1) mod (p)}\;\;\;\right) $, $ n = 0,1,\ldots, $ $ m,p\in \mathbb{N} $, where $ A\in(0,+\infty) $, $ x_{-i}^{(j)} $ are arbitrary positive numbers for $ i = 1,2,\ldots,m $ and $ j = 1,2,\ldots,p. $ We also give some numerical examples to demonstrate the effectiveness of the results obtained.

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