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.
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
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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