应用稳定流形定理研究二阶有理型非线性差分方程x n+1=a -bx n A +x n-1, n =0,1,2,…二周期正解的局部稳定性,其中 A,b >0,a ≥0均为实数,且初始条件 x -1和 x 0为任意正实数。结果表明,该二阶非线性差分方程的正平衡点是稳定的,最小二周期正解是不稳定的。%Using the stable manifold theorem,we studied the local stability of two periodic positive solutions of second order rational nonlinear difference equation x n+1 =a -bx n A +x n-1 , n =0,1,2,…where A,b >0,a ≥0 were real numbers,and initial conditions x -1 and x 0 were arbitrary positive real numbers.The results show that the positive equilibrium point of the second order nonlinear difference equation is stable,and the minimum two periodic positive solution is unstable.
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