Affiliation:
1. Department of Mathematics Hacι Bektaş Veli University Nevsehir Turkey
2. LMAM Laboratory Faculty of Exact Sciences and Informatics University of Jijel Jijel Algeria
Abstract
Abstract
In this paper, we consider a class of two-dimensional nonlinear difference equations system of second order, which is a considerably extension of some recent results in the literature. Our main results show that class of system of difference equations is solvable in closed form theoretically. It is noteworthy that the solutions of aforementioned system are associated with generalized Mersenne numbers. The asymptotic behavior of solution to aforementioned system of difference equations when a = b and p = 0 are also given. Finally, numerical examples are given to support the theoretical results presented in this paper.
Reference18 articles.
1. Abo-Zeid, R.: On the solutions of a higher order difference equation, Georgian Math. J. 27(2) (2020), 165–175.
2. Abo-Zeid, R.: Behavior of solutions of a second order rational difference equation, Math. Moravica 23(1) (2019), 11–25.
3. Din, Q.: Asymptotic behavior of an anti-competitive system of second-order difference equations, J. Egypt. Math. Soc. 24 (2016), 37–43.
4. Elabbasy, E. M.—El-Metwally, H.—Elsayed, E. M.: Qualititive behavior of higher order difference equations, Soochow J. Math. 33 (2007), 861–873.
5. Elsayed, E. M.—Alzahrani, F.—Abbas, I.—Alotaibi N. H.: Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence, J. Appl. Anal. Comput. 10(1) (2020), 282–296.