Basins of attraction of equilibrium points of second order difference equations

DOI10.1016/j.aml.2012.05.009zbMath1252.39018OpenAlexW2050439731MaRDI QIDQ714535

Mustafa R. S. Kulenović, Mirela Garić-Demirović, Mehmed Nurkanović

Publication date: 11 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.aml.2012.05.009

zbMATH Keywords

periodic solutionsdifference equationbasins of attractionglobal stable manifoldsnon-hyperbolic equilibrium points

Mathematics Subject Classification ID

Additive difference equations (39A10) Periodic solutions of difference equations (39A23) Stability theory for difference equations (39A30)

Related Items (8)

Global dynamics of cubic second order difference equation in the first quadrant ⋮ Global dynamics and bifurcations of certain second order rational difference equation with quadratic terms ⋮ The roles of conic sections and elliptic curves in the global dynamics of a class of planar systems of rational difference equations ⋮ Unnamed Item ⋮ 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 dynamic scenarios for competitive maps in the plane ⋮ Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation ⋮ Basins of attraction of equilibrium and boundary points of second-order difference equations

Uses Software

• Maple

Cites Work

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• Competitive-exclusion versus competitive-coexistence for systems in the plane
• Global stability, two conjectures and Maple
• The discrete dynamics of monotonically decomposable maps
• Periodic competitive differential equations and the discrete dynamics of competitive maps
• Competition systems with periodic coefficients: A geometric approach
• Global bifurcation for discrete competitive systems in the plane
• Asymptotic behavior of a competitive system of linear fractional difference equations
• A global attractivity result for maps with invariant boxes
• Asymptotic behavior of a system of linear fractional difference equations
• INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE
• Invariant Curves for Mappings
• Periodic Solutions of Periodic Competitive and Cooperative Systems
• Planar competitive and cooperative difference equations
• On second-order rational difference equations, Part 2
• Monotone maps: a review
• A rational difference equation

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