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Asymptotic stability for a class of nonlinear difference equations. (English) Zbl 1192.39015
Summary: We study the global asymptotic stability of the equilibrium point for the fractional difference equation $x_{n+1}=(ax_{n-l}x_{n-k})/(\alpha+bx_{n-s}+cx_{n-t})$, $n=0,1,\dots$, where the initial conditions $x_{-r},x_{-r+1},\dots,x_1,x_0$ are arbitrary positive real numbers of the interval $(0,\alpha/2a),l,k,s,t$ are nonnegative integers, $r=\max\{l,k,s,t\}$ and $\alpha,a,b,c$ are positive constants. Moreover, some numerical simulations are given to illustrate our results.

##### MSC:
 39A30 Stability theory (difference equations) 39A20 Generalized difference equations
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##### References:
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