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.


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