平方Logistic差分方程的全局吸引性

Global attractivity of square logistici difference equations

讨论平方Logistic差分方程xn + 1-xn=rnxn(1 +bxn -kn-cx2 n -kn) ,n =0 ,1 ,… ,其中 {rn}是非负实数列 ,{kn}是非负整数列 ,{n -kn}非单调递减 ,且limn→∞(n -kn) =∞ ,b∈ (-∞ ,∞ ) ,c∈ (0 ,+∞ ) ,给出了保证方程每一正解趋于正平衡点的充分条件 ,所得定理推广和改进了已有结果。

Square Logistic difference equation is studied x n+1 -x n=r nx n(1+bx n-k n -cx2 n-k n ), n=0,1,…,where ｛r n｝ is a sequence of nonnegative real numbers,｛k n｝ is a sequence of nonnegative intergers ,｛n-k n｝ is non decreasing ,lim n→∞(n-k n)=∞,b∈(-∞,+∞),c∈(0,+∞) .New sufficient conditions for the global attractivity of the positive equilibrium of equation is obtained, which improve some recent results in literature.