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The characteristics of a higher-order rational difference equation. (English) Zbl 1108.39006
The authors study the semicycles, periodicity, global stability and boundedness of the solutions of the rational difference equation $$ x_{n+1}=\frac{\alpha+\beta x_{n-k+1} + \gamma x_{n-2k+1}}{A+Bx_{n-k+1}},\quad n=0,1,2,\dots $$ where $A,~B$ and $\alpha,~\beta,~\gamma$ are positive, $k\in \{1,2,3,\dots\}$, and the initial conditions $x_{-2k+1},\dots,x_{-1},x_0$ are positive real numbers.

MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
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References:
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