Dynamical properties in a fourth-order nonlinear difference equation.

Chen, Yunxin; Li, Xianyi

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The authors consider the nonlinear difference equation $x_{n + 1} = α x_{n} + x_{n - k} f (x_{n - k}), n = 0, 1, \dots . 1 where α \in (0, 1), k \in {0, 1, \dots} and f \in C^{1} [[0, \infty), [0, \infty)] (0)$ with $f^{'} (x) < 0$ . They give sufficient conditions for the unique positive equilibrium of (0.1) 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.

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