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Global asymptotic behavior of $y_{n+1}=(py_{n}+y_{n - 1})/(r+qy_{n}+y_{n - 1})$. (English) Zbl 1149.39002
The authors study the global stability character of the equilibrium points and the period-two solutions of a certain rational difference equation with positive parameters and nonnegative initial conditions. It is shown that every solution of the equation converges to either the zero equilibrium, the positive equilibrium, or the period-two solution, for all values of parameters outside of a specific set. When the equilibrium points and period-two solution coexist, a precise description of the basins of attraction of all points are given.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Generalized difference equations
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