非线性时滞差分方程的全局吸引性

Global attractivity in a nonlinear delay difference equation

研究非线性差分方程 xn+ 1 =xnexp rn(1 - xn-k) / (1 +λxn-k) ,其中 { rn}是正实数列 ,λ∈(- 1 ,1 ) ,k为自然数。运用迭代方法 ,给出了保证其每一解 { xn}满足 limxn=1的若干充分条件 ,推广和改进了已有的结果。

Consider nonlinear delay difference equation x n+1 =x n exp r n(1-x n-k )/(1+λx x-k ),where｛r n｝is a sequence positive real number, λ∈(-1,1),k is a positive integer,this conclusion was drawn by a new method; some sufficient conditions that guarantee every positive solution to convergence to 1 as n→∞ were provided. Our results improved and generalized the known results.