Global attractivity of the equilibrium of a nonlinear difference equation. (English) Zbl 1014.39003

Summary: The authors consider the nonlinear difference equation \[ x_{n+1}=\alpha x_n + x_{n-k}f(x_{n-k}), \quad n=0, 1,\dots \] with \(f'(x)<0\). They give sufficient conditions for the unique positive equilibrium to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.


39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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