On the recursive sequence \(x_{n+1}=\frac{x+bx_n}{A+Bx^k_{n-1}}\)

DOI10.1016/J.AJMSC.2010.12.002zbMath1242.39013OpenAlexW2574123342MaRDI QIDQ531704

Yong-Cai Geng, Sumit K. Garg

Publication date: 19 April 2011

Published in: Arab Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ajmsc.2010.12.002

zbMATH Keywords

recursive sequenceglobal asymptotic stabilityequilibrium pointlocal asymptotic stabilityDifference equation

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Growth, boundedness, comparison of solutions to difference equations (39A22) Stability theory for difference equations (39A30)

Related Items (2)

Global stability of a third-order nonlinear system of difference equations with period-two coefficients ⋮ On the global dynamics of a rational difference equation with periodic coefficients

Cites Work

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• On the recursive sequence \(x_{n+1}=x_{n-1}/g(x_n)\)
• The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\)
• On the recursive sequence \(x_{n+1}=\frac{\alpha+\beta x_n}{Bx_n+Cx_{n-1}}\).
• Global behavior of \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).
• On rational recursive sequences
• Asyptotics for linear difference equations I:basic theory
• Stability of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)/(\gamma+x_{n-1})\)

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