一类二阶有理型差分方程二周期解的局部稳定性

Local Stability of Two Period Solutions of Second Order Rational Difference Equation

应用稳定流形定理研究了二阶有理型非线性差分方程x_(n+1)=α+x_(n-1)/x_n,n=0,1,…二周期正解的局部稳定性,这里α=1且初始条件x-1和x0为任意正实数,证明了在一定条件下方程的最小二周期解是稳定的.

Using the stable manifold theorem,we study the local stability of two period solutions of second order rational difference equation xn＋1=α＋xn-1xn ,n=0,1,…,whereα=1 and the initial condition x-1 and x0 are arbitrary positive real numbers. The result proves that the minimum two periodic solutions are stable under some conditions.