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On the difference equation $yn+1=\frac{α+{ynp}}{β{yn-1p}} -\frac{γ+{yn-1p}}{β{ynp}}$

In: Mathematica Slovaca, vol. 61, no. 6
Ilhan Öztürk - Saime Zengin

Details:

Year, pages: 2011, 921 - 932
Keywords:
difference equations, global stability, period-two solutions
About article:
In this paper, we investigate the global stability and the periodic nature of solutions of the difference equation

$$ yn+1=\frac{α+{ynp}}{β{yn-1p}} -\frac{γ+{yn-1p}}{β{ynp}}, n=0,1,2,… $$

where $α,β,γ\in (0,∞ )$, $α (1-p)-γ>0$, $0n\neq 0$ for $n=-1,0,1,2,… $ and the initial conditions $y-1$, $y0$ are arbitrary positive real numbers. We show that the equilibrium point of the difference equation is a global attractor with a basin that depends on the conditions of the coefficients.
How to cite:
ISO 690:
Öztürk, I., Zengin, S. 2011. On the difference equation $yn+1=\frac{α+{ynp}}{β{yn-1p}} -\frac{γ+{yn-1p}}{β{ynp}}$. In Mathematica Slovaca, vol. 61, no.6, pp. 921-932. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0058-6

APA:
Öztürk, I., Zengin, S. (2011). On the difference equation $yn+1=\frac{α+{ynp}}{β{yn-1p}} -\frac{γ+{yn-1p}}{β{ynp}}$. Mathematica Slovaca, 61(6), 921-932. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0058-6
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