Invariant curves for planar competitive and cooperative maps

DOI10.1080/10236198.2018.1438418zbMath1391.39022OpenAlexW2791656736MaRDI QIDQ4576739

Orlando Merino, Mustafa R. S. Kulenović

Publication date: 10 July 2018

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2018.1438418

zbMATH Keywords

stabilityinvariant setperiodic solution

Mathematics Subject Classification ID

Additive difference equations (39A10) Dynamical aspects of attractors and their bifurcations (37G35) Stability theory for difference equations (39A30)

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Cites Work

• The dynamics of the Hénon map
• Competitive-exclusion versus competitive-coexistence for systems in the plane
• \(P\)-arcs in strongly monotone discrete-time dynamical systems
• Basins of attraction for two-species competitive model with quadratic terms and the singular Allee effect
• Convergence to equilibrium on invariant \(d\)-hypersurfaces for strongly increasing discrete-time semigroups
• Dynamics of a two-dimensional competitive system of rational difference equations with quadratic terms
• Two species competitive model with the allee effect
• Global bifurcation for discrete competitive systems in the plane
• Convexity of the carrying simplex for discrete-time planar competitive Kolmogorov systems
• 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
• On the Global Behavior of Solutions to a Planar System of Difference Equations
• Invariant Curves for Mappings
• Planar competitive and cooperative difference equations
• On the Stable Manifold Theorem
• On the Behavior of Invariant Curves Near a Hyperbolic Point of a Surface Transformation
• The general properties of dicrete-time competitive dynamical systems
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