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Zbl 1149.39002
Brett, A.; Kulenović, M.R.S.
Global asymptotic behavior of $y_{n+1}=(py_{n}+y_{n - 1})/(r+qy_{n}+y_{n - 1})$. (English)
[J] Adv. Difference Equ. 2007, Article ID 41541, 22 p. (2007). ISSN 1687-1847/e

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.
[B. G. Pachpatte (Aurangabad)]

MSC 2000:: *39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: global stability; equilibrium points; period-two solutions; rational difference equation; basins of attraction

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