A generalized two-dimensional system of higher order recursive sequences. Issue 2 (1st February 2020)

• Record Type: Journal Article
• Authors: Folly-Gbetoula, M.; Nyirenda, D.
• Is Part Of: Journal of difference equations and applications. Volume 26:Issue 2(2020)
• Page Start: 244
• Page End: 260
• Publication Date: 2020-02-01
• Subjects: Difference equation -- symmetry -- reduction -- periodicity; 39A10 -- 39A13 -- 39A99; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2020.1718667
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : In this paper, we find exact formulas for the solutions of the system of ( k + 1)th-order difference equations x n + 1 = x n − k + 1 y n − k y n ( a n + b n x n − k + 1 y n − k ), y n + 1 = x n − k y n − k + 1 x n ( c n + d n x n − k y n − k + 1 ), where ( a n ) n ∈ N 0, ( b n ) n ∈ N 0 are non-zero real sequences. The method involves deriving non-trivial symmetries for the equations. We further provide sufficient conditions for the existence of periodic solutions. The results in this paper generalize some work in the literature.