Dynamic behavior of a nonlinear rational difference equation and generalization

DOI10.1186/1687-1847-2011-36zbMath1271.39011OpenAlexW2112159640WikidataQ59268452 ScholiaQ59268452MaRDI QIDQ355168

Mohammad Hasan, M. Dambrine

Publication date: 24 July 2013

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2011-36

zbMATH Keywords

global stabilitypositive solutionnonlinear rational difference 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)

Cites Work

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• Global asymptotic stability and oscillation of a family of difference equations
• On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\).
• On the recursive sequence \(x_n = \frac{ax_{n-1}+bx_{n-2}}{c+dx_{n-1}x_{n-2}}\)
• Global asymptotic stability of a higher order nonlinear difference equation
• The global attractivity of the rational difference equation \(y_n = \frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}\)
• Global attractivity for a family of nonlinear difference equations
• Qualitative properties for a fourth-order rational difference equation

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