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Further properties of the rational recursive sequence \(x_{n+1}=\frac {ax_{n-1}} {b+cx_n x_{n-1}}\). (English) Zbl 1131.39003
Summary: We consider the difference equation
\[ x_{n+1}=\frac{ax_{n-1}}{b+cx_n x_{n-1}}\,\quad n=0,1,\dots\tag{E} \]
with positive parameters \(a\) and \(c\), negative parameter \(b\) and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation (E).

MSC:
39A10 Additive difference equations
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