We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: x n+1 = (α 1 + β 1 x n−1)/(a 1 + b 1 y n), y n+1 = (α 2 + β 2 y n−1)/(a 2 + b 2xn), where the parameters αi, βi, ai, and bi for i ∈ {1,2} and initial conditions x0, x−1, y0, and y−1 are positive real numbers. Some numerical examples are given to verify our theoretical results.
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机译:我们研究以下有理差分方程组的正平衡的有界性,持久性,存在性和唯一性,正平衡点的局部和全局行为以及正解的收敛速度:x n + 1 =(α1 +β 1 xn-1)/(a 1 + b 1 yn),y n + 1 =(α2 +β2 yn-1)/ (a em> 2 + b em> 2 x em> n em>),其中参数α em> i em>,β em> i em>, a em> i em> sub>和 b em> i em>∈{1,2}的 i em> sub>和初始条件 x em> 0 sub>, x em> -1 sub>, y em> 0 sub>和 y em> -1 sub>是正实数。给出了一些数值例子来验证我们的理论结果。
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