Global Analysis of Solutions of a New Class of Rational Difference Equation - American Journal of Computational Mathematics

AJCM > Vol.7 No.4, December 2017

American Journal of Computational Mathematics

Volume 7, Issue 4 (December 2017)

ISSN Print: 2161-1203 ISSN Online: 2161-1211

Google-based Impact Factor: 0.42 Citations

Global Analysis of Solutions of a New Class of Rational Difference Equation ()

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Download as PDF (Size: 1299KB) PP. 495-503

DOI: 10.4236/ajcm.2017.74036 937 Downloads 1,859 Views

Author(s)

O. Moaaz¹, E. M. Elabbasy¹, Sh. Alsaeed²

Affiliation(s)

¹Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
²Department of Mathematics, The Faculty of Education, Al al-Bayt University, Mafraq, Jordan.

ABSTRACT

The study suggests asymptotic behavior of the solution to a new class of difference equations:

. where a, b_i, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ_-j, ψ_-j+1, · · ·, ψ₀ are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.

KEYWORDS

Difference Equation, Stability, Boundedness, Globale Stability and Periodicity

Share and Cite:

Moaaz, O. , Elabbasy, E. and Alsaeed, S. (2017) Global Analysis of Solutions of a New Class of Rational Difference Equation. American Journal of Computational Mathematics, 7, 495-503. doi: 10.4236/ajcm.2017.74036.

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