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Dynamical behavior of a P-dimensional system of nonlinear difference equations

  • Yacine Halim EMAIL logo , Asma Allam and Zineb Bengueraichi
Published/Copyright: August 4, 2021
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 4

Abstract

In this paper, we study the periodicity, the boundedness of the solutions, and the global asymptotic stability of the positive equilibrium of the system of p nonlinear difference equations

xn+1(1)=A+xn−1(1)xn(p),xn+1(2)=A+xn−1(2)xn(p),…,xn+1(p−1)=A+xn−1(p−1)xn(p),xn+1(p)=A+xn−1(p)xn(p−1)

where n ∈ ℕ0, p ≥ 3 is an integer, A ∈ (0, +∞) and the initial conditions x−1(j), x0(j), j = 1, 2, …, p are positive numbers.

Keywords: System of difference equations; periodic solutions; boundedness; the asymptotic behavior; stability
MSC 2010: Primary 39A10; Secondary 40A05

This work was supported by Directorate General for Scientific Research and Technological Development (DGRSDT), Algeria.

  1. (Communicated by Michal Fečkan)

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Received: 2020-04-14
Accepted: 2020-10-21
Published Online: 2021-08-04
Published in Print: 2021-08-26

© 2021 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular Papers
  2. Quasi-decompositions and quasidirect products of Hilbert algebras
  3. Residuation in finite posets
  4. On a problem in the theory of polynomials
  5. Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
  6. Mapping properties of the Bergman projections on elementary Reinhardt domains
  7. Lemniscate-like constants and infinite series
  8. On the Oscillation of second order nonlinear neutral delay differential equations
  9. Oscillation theorems for certain second-order nonlinear retarded difference equations
  10. De la Vallée Poussin inequality for impulsive differential equations
  11. Hs-Boundedness of a class of Fourier Integral Operators
  12. Dynamical behavior of a P-dimensional system of nonlinear difference equations
  13. Some inequalities for exponentially convex functions on time scales
  14. Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
  15. The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
  16. A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
  17. Simulations of nonlinear parabolic PDEs with forcing function without linearization
  18. An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
  19. A relationship between the category of chain MV-algebras and a subcategory of abelian groups
https://doi.org/10.1515/ms-2021-0030
Keywords for this article
System of difference equations; periodic solutions; boundedness; the asymptotic behavior; stability

Articles in the same Issue

  1. Regular Papers
  2. Quasi-decompositions and quasidirect products of Hilbert algebras
  3. Residuation in finite posets
  4. On a problem in the theory of polynomials
  5. Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
  6. Mapping properties of the Bergman projections on elementary Reinhardt domains
  7. Lemniscate-like constants and infinite series
  8. On the Oscillation of second order nonlinear neutral delay differential equations
  9. Oscillation theorems for certain second-order nonlinear retarded difference equations
  10. De la Vallée Poussin inequality for impulsive differential equations
  11. Hs-Boundedness of a class of Fourier Integral Operators
  12. Dynamical behavior of a P-dimensional system of nonlinear difference equations
  13. Some inequalities for exponentially convex functions on time scales
  14. Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
  15. The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
  16. A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
  17. Simulations of nonlinear parabolic PDEs with forcing function without linearization
  18. An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
  19. A relationship between the category of chain MV-algebras and a subcategory of abelian groups
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