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Global attractivity of a higher order nonlinear difference equation. (English) Zbl 1081.39005

The authors investigate the global attractivity of a positive equlibrium of equations of the form \(y_{n+1} = (p+qy_n)/(1+y_n+ry_{n-k})\), \(n=0,1,\dots\), where \(p,q,r\) are positive numbers. They show that the unique positive equilibrium globally attracts all positive values of the parameters. The obtained results improve previous ones in this direction.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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References:

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