Global dynamics of a competitive system of rational difference equations in the plane

DOI10.1155/2009/132802zbMath1187.39024OpenAlexW2000143488WikidataQ59254866 ScholiaQ59254866MaRDI QIDQ963074

Mustafa R. S. Kulenović, Senada Kalabušić, Esmir Pilav

Publication date: 8 April 2010

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

Full work available at URL: https://doi.org/10.1155/2009/132802

zbMATH Keywords

manifoldsasymptotic stabilityglobal stabilitysaddle pointsglobal dynamicsrational difference equationssystems of difference equationsbasins of attractionsnonhyperbolic equilibrium points

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Multiplicative and other generalized difference equations (39A20) Stability theory for difference equations (39A30)

Related Items (15)

Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model ⋮ A variant of the Krein–Rutman theorem for Poincaré difference equations ⋮ Dynamics of a modified Nicholson-Bailey host-parasitoid model ⋮ Global dynamics of some systems of higher-order rational difference equations ⋮ The roles of conic sections and elliptic curves in the global dynamics of a class of planar systems of rational difference equations ⋮ Dynamics of a two-dimensional system of rational difference equations of Leslie-Gower type ⋮ Global dynamical properties of rational higher-order system of difference equations ⋮ Behavior of an exponential difference equations system ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Qualitative behavior of two systems of higher‐order difference equations ⋮ Global dynamics of a competitive system of rational difference equations ⋮ Local dynamics and global attractivity of a certain second-order quadratic fractional difference equation ⋮ Global dynamics of a \(3 \times 6\) system of difference equations ⋮ Dynamic characteristics of four systems of difference equations with higher order

Cites Work

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• Competitive-exclusion versus competitive-coexistence for systems in the plane
• The discrete dynamics of monotonically decomposable maps
• Global behavior of four competitive rational systems of difference equations in the plane
• Periodic competitive differential equations and the discrete dynamics of competitive maps
• Competition systems with periodic coefficients: A geometric approach
• Mutual exclusion versus coexistence for discrete competitive systems
• Geometry of exclusion principles in discrete systems
• A coupled system of rational difference equations
• Global asymptotic behavior of a two-dimensional difference equation modelling competition
• Global bifurcation for discrete competitive systems in the plane
• Asymptotic behavior of a competitive system of linear fractional difference equations
• Asymptotic behavior of a system of linear fractional difference equations
• INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE
• Rational systems in the planeEdited by Gerry LadasIn this section, we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas: gladas@math.uri.edu
• Invariant Curves for Mappings
• Periodic Solutions of Periodic Competitive and Cooperative Systems
• Planar competitive and cooperative difference equations

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