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The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\). (English) Zbl 1131.39006
For the equation in the title with \(0< k< m\) it is shown that all positive solutions converge to the equilibrium 1. Two conjectures concerning the asymptotic stability for positive solutions of more general difference equations are given.

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
Full Text: DOI
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