迭代序列x_(n+1)=(α+βx_(n-k))/(1+sum from i=1 to k x_(n-i+1)~γ)的全局性质

Global Behaviour of Recursive Sequence x_(n+1)=(α+βx_(n-k))/(1+sum from i=1 to k x_(n-i+1)~γ)

通过函数f（x）=（α＋βx）/（1＋kx^γ）在[0,＋∞]上的单调性，并利用上下极限方法得到了非线性差分方程xn＋1=（α＋βxn-k）/（1＋^k∑i=1x^γn-i＋1）正平衡点的全局吸引性，同时还得到正振动解的半循环分布．其中α〉0,0〈β〈1,0〈γ≤1,k∈N,x-k…x0是任意非负实数．

The Global attractivity of the positive equilibrium to the following nonlinear difference equations xn＋1=（α＋βxn-k）/（1＋^k∑i=1x^γn-i＋1）is investigated by using the lower-upper limit methods and monotone character of the functionf（x） f（x）=（α＋βx）/（1＋kx^γ）在[0,＋∞].The distributions of semicycles to the positive oscillatory solutions are also obtained,where （α〉0,0〈β〈1,0〈γ≤1,k∈N）