On the difference equation $x_{n+1}=\dfrac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}} $

DOI10.21136/mb.2008.134057zbMath1199.39028OpenAlexW2269375186MaRDI QIDQ3392720

Hamdy A. El-Metwally, Elsayed M. Elsayed, Elmetwally M. Elabbasy

Publication date: 17 August 2009

Full work available at URL: https://eudml.org/doc/32689

zbMATH Keywords

stabilityglobal convergenceboundednessperiodic solutionrecursive sequencerational difference equation

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Growth, boundedness, comparison of solutions to difference equations (39A22) Periodic solutions of difference equations (39A23) Stability theory for difference equations (39A30)

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Global asymptotic stability for quadratic fractional difference equation ⋮ Analytical solution of a rational difference equation ⋮ A solution form of a class of higher-order rational difference equations ⋮ Qualitative behavior of difference equation of order two ⋮ On a New Class of Rational Difference Equation zn+1 = azn + bzn-k + (α + βzn−k)/ (A+ Bzn−k)

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