International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 7, Issue 5 (May 2020), Pages: 66-78

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 Original Research Paper

 Title: Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

 Author(s): M. Ghazel 1, *, T. Alraqad 1, F. Kadhi 2

 Affiliation(s):

 1Mathematics Department, University of Ha’il, Ha’il, Saudi Arabia
 2Ecole Nationale des Sciences de l 'Informatiques (ENSI), Manouba University, Manouba, Tunisia

  Full Text - PDF          XML

 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-1125-798X

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.05.009

 Abstract:

This work is devoted to present a study of the class of the difference equations Xn+1= Xn-2q+1/A+BXn-2qXn-q+1, q=1,2,… with arbitrary initial data, where  and  are arbitrary parameters, and  is an arbitrary nonnegative integer. We present a detailed investigation of the behavior of the solution, including their dependence on parameters and initial conditions. Local and global stabilities of the equilibrium points are discussed. The existence of a periodic solution is studied. Numerical simulations are given to assure the correctness of the analytical results. This study improves and surpasses studies of several forms of difference equations that have been investigated earlier by many researchers. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Difference equations, Analytical study, Good set, Asymptotic behavior, Periodicity

 Article History: Received 25 October 2019, Received in revised form 10 February 2020, Accepted 14 February 2020

 Acknowledgment:

The authors thank the Deanship of Research at the University of Ha’il, Saudi Arabia, for funding this work under Grant no. 0160847. The authors also thank the referees for their valuable comments, which helped to improve the paper.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Ghazel M, Alraqad T, and Kadhi F (2020). Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1. International Journal of Advanced and Applied Sciences, 7(5): 66-78

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8

 Tables

 No Table

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