Qualitative behavior and solution of a system of three‐dimensional rational difference equations. (6th February 2022)

• Record Type: Journal Article
• Authors: Elsayed, E. M.; Alshareef, A.; Alzahrani, Faris
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 9(2022)
• Page Start: 5456
• Page End: 5470
• Publication Date: 2022-02-06
• Subjects: difference equation -- equilibrium points -- global attractor -- periodicity -- stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8120
• Languages: English
• ISSNs: 0170-4214

Abstract

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.