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Title: On the difference equation Xn+1 = α+ Xpn/Xpn−1
Other Titles: On the difference equation x_ {n+ 1}=\ alpha+\ frac {{x_n^ p}}{{x_ {n-1}^ p}}
Authors: Aloqeili, Mohammad
Issue Date: 1-May-2006
Publisher: Applied Mathematics and Computation
Source: 34
Abstract: The dynamics of the difference equation Xn+1 = α+ Xpn/Xpn−1 , with p ∈ (0, 1) and α ∈ [0, ∞) was studied first. Our aim was to study the asymptotic behaviour of the rational difference equation Xn+1 = α+ Xp/pn Xn-k
We find conditions for the global asymptotic stability of the unique negative equilibrium y ¼ 1 þ A of the equation ynþ1 ¼ A þ yn ynk ; ð0:1Þ where yk,yk+1,...,y0 2 (0,1), A < 0 and k 2 {1, 2, 3, 4,...}.
Description: Journal of Applied Mathematics & Computing, Vol. 25 (2007), No. 1 - 2, pp. 375 - 382
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