## On global stability in a nonlinear discrete model.(English)Zbl 0842.39005

For difference equations of the form $\mu \Delta x_n= -x_{n+ 1}+ f(x_{n- m}), \qquad n\in \mathbb{N}\cup \{0\}$ with continuous $$f: \mathbb{R}\to \mathbb{R}$$, parameter $$\mu>0$$ and delay $$m\in \mathbb{N}$$, the global attractivity of a stationary solution is studied by means of the interval maps described by the functions $$f(x)$$ and $$F(x):= {1\over {\mu+1}} f(x)$$, respectively. Some sufficient and some necessary conditions are derived and applied to particular model equations related to population dynamics.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39A10 Additive difference equations 92D25 Population dynamics (general)
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### References:

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