Asymptotic Behavior of the Solutions of Difference Equation System of Exponential Form

Abstract

In this paper, we study the boundedness character and persistence, local and global behavior, and rate of convergence of positive solutions of following system of rational difference equations [Formula: see text] wherein the parameters [Formula: see text] for [Formula: see text] and the initial conditions [Formula: see text] are positive real numbers. Some numerical examples are given to verify our theoretical results.

Solution Expressions of Discrete Systems of Difference Equations

“…Many of authors investigated the behavior of nonlinear systems of di erence equations when the solutions are di cult to obtain. For example, Khaliq and Zubair in [4] studied properties of solutions such as persistence, boundedness, global stability, and locally asymptotically stable of equilibrium point…”

Asymptotic behavior of a difference equation model in exponential form

“…Difference equations (systems) play a crucial role in the development of a variety of disciplines (see, e.g., previous studies 1‐38 and references cited therein). The exponential form is one of the most diverse types of difference equations.…”

“…Khaliq et al 31 examined the system $$$$ {u}_{n+1}=\frac{a_1+{a}_2{e}^{-{v}_n}}{A_1+{A}_2{u}_n},{v}_{n+1}=\frac{b_1+{b}_2{e}^{-{w}_n}}{B_1+{B}_2{v}_n},{w}_{n+1}=\frac{c_1+{c}_2{e}^{-{u}_n}}{C_1+{C}_2{w}_n}, $$$$ where the parameters and initials are non‐negative real numbers. Papaschinopoulos et al 35 deal with the behavior of systems: …”

“…where the initials u −1 , u 0 , v −1 , and v 0 and the parameters 𝜆, 𝜇, 𝛾, 𝜇 1 , 𝛾 1 , and 𝜆 1 are positive real numbers. Khaliq et al 31 examined the system…”