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Dynamics of a rational difference equation. (English) Zbl 1100.39002
Author’s summary: We investigate the solution of the difference equation \(x_{n+1}= \frac {x_{n-1}}{a-x_{n-1}x_{n}}\), where \(n=0,1,2,\ldots,\) where \(x_{-1}, x_{0} \in {\mathbb R}\) and \(a > 0\). Moreover, we discuss the stability properties and semi-cycle behavior of this solution.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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