Solution Expressions of Discrete Systems of Difference Equations

Abstract

In this paper, we obtain the solution forms of fifth order systems of rational difference equations $P_{n+1}=P_{n4}{S}_{n2}{Q}_n/S_{n-3}{Q}_{n-1}\left(1\pm P_{n-4}{S}_{n-2}{Q}_n\right),$ $Q_{n+1}=Q_{n-4}{P}_{n-2}{S}_n/P_{n-3}{S}_{n-1}\left(1\pm Q_{n-4}{P}_{n-2}{S}_n\right),$ and $S_{n+1}=S_{n-4}{Q}_{n-2}{P}_n/Q_{n-3}{P}_{n-1}\left(1\pm S_{n-4}{Q}_{n-2}{P}_n\right)$ . Where the initial values are nonzero real numbers. Numerical examples are also provided.