Qualitative behavior and solution of a system of three‐dimensional rational difference equations

Abstract

In this paper, we construct the solutions expressions for a system of three‐dimensional nonlinear difference equations Rn+1=a1Tn−1Sn−1Rn−1+Sn−1+Tn−1,Sn+1=a2Tn−1Rn−1Rn−1+Sn−1+Tn−1,Tn+1=a3Rn−1Sn−1Rn−1+Sn−1+Tn−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.

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…where α 1 , α 2 and α 3 satisfy the same conditions as mentioned in (9). Subsequently, the explicit closed-form expression for the general solution of the first (respectively, second) linear difference equation of System (8) is given by:…”

“…A particularly active area of research centers on the pursuit of closed-form solutions to nonlinear systems of difference equations, to enhance our understanding of dynamic systems and refine predictions with greater precision. (see, [8][9][10][11][12][13]). Many researchers have made significant contributions to unraveling the behavior of solved difference equations and systems, shedding light on their dynamics and stability properties.…”

Solution Expressions of Discrete Systems of Difference Equations

“…Elsayed et al [6] obtained the solution expressions and studied the behavior of three-dimensional systems of difference equations…”