Attractivity and global stability for linearizable difference equations

DOI10.1016/j.camwa.2008.10.064zbMath1186.39025OpenAlexW2013667117MaRDI QIDQ971671

E. J. Janowski, Mustafa R. S. Kulenović

Publication date: 16 May 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.10.064

zbMATH Keywords

stabilitydifference equationsattractivitynon-autonomouslinearized

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Stability theory for difference equations (39A30)

Related Items (21)

Global dynamics of cubic second order difference equation in the first quadrant ⋮ Global asymptotic stability for quadratic fractional difference equation ⋮ Global dynamics of quadratic second order difference equation in the first quadrant ⋮ Global dynamics of rational difference equations \(x_{n + 1} = \left(x_n + x_{n - 1}\right) / \left(q + y_n y_{n - 1}\right)\) and \(y_{n + 1} = \left(y_n + y_{n - 1}\right) / \left(p + x_n x_{n - 1}\right)\) ⋮ Global asymptotic stability for discrete single species population models ⋮ On global asymptotic stability of nonlinear higher-order difference equations ⋮ Stability, Neimark-Sacker bifurcation, and approximation of the invariant curve of certain homogeneous second-order fractional difference equation ⋮ Global behavior of certain nonautonomous linearizable three term difference equations ⋮ Forbidden sets and stability in some rational difference equations ⋮ Naimark-Sacker bifurcation of second order rational difference equation with quadratic terms ⋮ Global asymptotic behavior of \(y_{n+1}=(py_{n}+y_{n - 1})/(r+qy_{n}+y_{n - 1})\) ⋮ BEHAVIOR OF SOLUTIONS OF A RATIONAL THIRD ORDER DIFFERENCE EQUATION ⋮ Global behavior of a third order difference equation with quadratic term ⋮ Local dynamics and global attractivity of a certain second-order quadratic fractional difference equation ⋮ Global behavior of a rational second order difference equation ⋮ Basins of attraction of equilibrium and boundary points of second-order difference equations ⋮ Existence of a period-two solution in linearizable difference equations ⋮ Behavior of solutions of a second order rational difference equation ⋮ Unnamed Item ⋮ Global period-doubling bifurcation of quadratic fractional second order difference equation ⋮ Global behavior and oscillation of a third order difference equation

Uses Software

• Maple

Cites Work

• Unnamed Item
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• Global stability, two conjectures and Maple
• Geometric stability conditions for higher order difference equations
• The global attractivity of difference equations of nonincreasing nonlinearities with applications.
• Invariants and related Liapunov functions for difference equations
• Rate of convergence of solutions of rational difference equation of second order
• Invariants for some rational recursive sequences with periodic coefficients
• On the boundedness character of rational equations, part 1
• A note on unbounded solutions of a class of second order rational difference equations
• A rational difference equation

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