Global asymptotic stability of \(x_{n+1}=F(x_n)g(x_{n-1})\). (English) Zbl 0963.39006

Li, Longtu

Ann. Differ. Equations 14, No. 3, 518-525 (1998).

Summary: We obtain sufficient conditions for the global asymptotic stability of the difference equation \[ x_{n+1}= F(x_n)g(x_{n-1}), \quad n=0,1,2, \dots. \] We also apply our results to the rational recursive sequence \[ x_{n+1}= {a+bx^2_n \over c+x^2_{n-1}}, \quad n=0,1, \dots. \]

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

global asymptotic stability; difference equation; rational recursive sequence