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Global asymptotic stability of the nonlinear difference equation \(x_{n+1}=f(x_n,x_{n-k})\). (English) Zbl 1141.39305

Summary: A nonlinear difference equation \(x_{n+1}=f(x_n, x_{n-k}),\) \(n=0, 1,\dots\), where \(x_{-k}, x_{-k+1}, \dots, x_0 \in (0, +\infty)\) is considered. The sufficient conditions are obtained under which the unique positive equilibrium of this equation is globally asymptotically stable.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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