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