Global behavior of P-dimensional difference equations system

Khelifa Amira; Halim Yacine

doi:10.3934/era.2021029

Article Contents

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

This issue Previous Article Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise Next Article A multigrid based finite difference method for solving parabolic interface problem

Global behavior of P-dimensional difference equations system

Khelifa Amira^1, and
Halim Yacine^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

^* Corresponding author: Yacine Halim
^* Corresponding author: Yacine Halim

Received: January 2021

Revised: March 2021

Early access: April 15, 2021

Published online: April 15, 2021

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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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Mathematics Subject Classification: Primary: 39A10; Secondary: 40A05.

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Figure 1. The plot of system (23) with $ A = 1.2>1 $

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Figure 2. The plot of system (23) with $ A = 1 $

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Figure 3. The plot of system (23) with $ A = 0.9<1 $

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Figure 4. The plot of system (24) with $ A = 1.4>1 $

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Figure 5. The plot of system (24) with $ A = 1 $

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Figure 6. The plot of system (24) with $ A = 0.7<1 $

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