Qualitative behavior and solution of a system of three‐dimensional rational difference equations. (6th February 2022) - Elsayed, E. M.; Alshareef, A.; Alzahrani, Faris
Abstract : In this paper, we construct the solutions expressions for a system of three‐dimensional nonlinear difference equations R n + 1 = a 1 T n − 1 S n − 1 R n − 1 + S n − 1 + T n − 1, S n + 1 = a 2 T n − 1 R n − 1 R n − 1 + S n − 1 + T n − 1, T n + 1 = a 3 R n − 1 S n − 1 R n − 1 + S n − 1 + T n − 1 . In addition, we prove some properties of the proposed system such as boundedness and periodicity of the positive solutions and the global asymptotic stability of the equilibrium points. Finally, we present some numerical examples in order to illustrate the theoretical results.