带周期参数的差分方程组的全局性质

Global Character of System of Difference Equations with Periodic Parameters

研究差分方程组xn+1=An+xn-1/yn,yn+1=Bn+yn-1/xn,n=0,1,…,的全局性质,其中参数An,Bn∈(1,+∞)且是二周期序列,初始值x-1,y-1∈(0,+∞),x0,y0∈(0,+∞)。通过研究奇偶解子列的有界性来进一步研究其收敛性,最终得到了方程组的每个正解都收敛于二周期解的结论,并且给出了不变区域的充分条件。

This paper mainly investigates the global character of a system of difference equations xn+1= An +xn-1 yn ,yn+1 = Bn +yn-1 xn ,n = 0,1,…,in which parameters An ,Bn ∈ (1,+ ∞)are period-2 sequences and the initial conditions x-1 ,y-1 ∈ (0,+∞),x 0 ,y 0 ∈ (0,+∞).The boundedness of the solutions of odd sub-columns and even sub-columns are used to further study their convergence.Finally,the positive solu-tion of the system of difference equations converge to unique period-2 solution and a sufficient condition for constant region are given.