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Global asymptotic stability in a rational recursive sequence. (English) Zbl 1071.39018
The global stability of the difference equation $x_{n}=\frac{a+bx_{n-1}+cx_{n-1}^2}{d-x_{n-2}}, \quad n=1,2,\dots$ where $$a,b\geq 0$$ and $$c,d>0$$ is studied. It is shown that one nonnegative equillibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive solution of the equation in the basin exponentially converges to the attractor.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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##### References:
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