Global asymptotic behavior of the difference equation \(y_{n+1}=\frac{\alpha \cdot \text{e}^{-(ny_n+(n-k)y_{n-k})}}{\beta +ny_n+(n-k)y_{n-k}}\)

DOI10.1016/j.aml.2008.06.037zbMath1184.39008OpenAlexW2095575222MaRDI QIDQ1021893

J. Martínez

Publication date: 9 June 2009

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2008.06.037

zbMATH Keywords

boundednesspositive solutionsglobal asymptotic stabilityrational difference equationslocal asymptotic stability

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 (4)

Investigation of the global dynamics of two exponential-form difference equations systems ⋮ Behavior of solutions of a discrete population model with mutualistic interaction ⋮ Asymptotic and boundedness behaviour of a rational difference equation ⋮ Global dynamics of higher-order exponential systems of difference equations

Cites Work

• Unnamed Item
• On the difference equation \(y_{n+1} = \frac {\alpha +\beta e^{-y_n}}{\gamma +y_{n-1}}\)
• The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
• On the recursive sequence \(y_{n+1}=(p+y_{n-1})/(qy_n+y_{n-1})\)
• On the difference equation \(x_{n+1}=\alpha+\beta x_{n-1}e^{-x_n}\).
• Global behavior of \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).
• On the Trichotomy Character of x n +1 =(α+β x n +γ x n −1 )/( A + x n )

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