非线性平均增长率的离散Logistic方程的全局吸引性

GLOBAL ATTRACTIVITY OF A LOGISTIC EQUATION WITH NONLINEAR AVERAGE GROWTH

研究一类非线性 Logistic方程 :xn+ 1=xnexp[rn(1 -axn-bx2n) ],n=0 ,1 ,2…的全局吸引性 ,其中 {rn}为一个非负数列 ,a,b>0 ,x0 >0 ,获得了方程的所有解 {xn}收敛于正平衡常数 N=-a+a2 +4 b2 a 的充分条件 ,所得结果推广了已有文献的一些结果 .

This paper considered the nonlinear difference equati on: x n+1 =x n exp( r n(1-ax n-bx 2 n)),n=0,1,2..., where {r n} is a sequence of non-negative numbers and a,b∈(0,+∞),x 0>0. We obtained a sufficient condition for all solutions of the equation t ending to the positive equilibrium solution N as n→∞.