The global attractivity of a higher order rational difference equation

DOI10.1016/j.jmaa.2006.02.087zbMath1112.39002OpenAlexW2017702502MaRDI QIDQ865311

Stevo Stević, Kenneth S. Berenhaut

Publication date: 14 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.02.087

zbMATH Keywords

symmetrystabilitypositive solutionrational difference equationsemi-cycles

Mathematics Subject Classification ID

Related Items (27)

Asymptotic behaviour of solutions to difference equations involving ratios of elementary symmetric polynomials ⋮ On the period-two cycles of \(x_{n + 1} = (\alpha + \beta x_n + \gamma x_{n - k})/(A + Bx_n + Cx_{n - k})\) ⋮ Global asymptotic stability of a higher order rational difference equation ⋮ Dynamical properties of a class of higher-order nonlinear difference equations ⋮ A Prešić type contractive condition and its applications ⋮ On the rational difference equation \(x_{n}=1+\frac{(1-x_{n-k})(1-x_{n-l})(1-x_{n-m})}{x_{n-k}+x_{n-l}+x_{n-m}}\) ⋮ Linear difference equations mod 2 with applications to nonlinear difference equations1 ⋮ On some \(k\)-dimensional cyclic systems of difference equations ⋮ Global behavior of two families of nonlinear symmetric difference equations ⋮ On a system of difference equations ⋮ A new part-metric-related inequality chain and an application ⋮ Stability of solutions for a family of nonlinear difference equations ⋮ GLOBAL ASYMPTOTIC STABILITY FOR GENERAL SYMMETRIC RATIONAL DIFFERENCE EQUATIONS ⋮ Existence of nontrivial solutions of a rational difference equation ⋮ About the stability and positivity of a class of discrete nonlinear systems of difference equations ⋮ Global asymptotic stability in a class of difference equations ⋮ Some contractive type mappings and their applications to difference equations ⋮ Global stability of some symmetric difference equations ⋮ Part-metric and its applications in discrete systems ⋮ General form of some rational recursive sequences ⋮ Eventually constant solutions of a rational difference equation ⋮ Global stability of a rational symmetric difference equation ⋮ On the global asymptotic stability of a second-order system of difference equations ⋮ Global asymptotic stability of a family of difference equations ⋮ Global asymptotic stability of a family of nonlinear difference equations ⋮ On a conjecture for a higher-order rational difference equation ⋮ Global stability for a delay difference equation

Cites Work

• Two rational recursive sequences
• Qualitative properties for a fourth-order rational difference equation
• Global behavior for a fourth-order rational difference equation
• The global attractivity of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$
• Progress Report on Rational Difference Equations
• Unnamed Item

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