Convexity of the carrying simplex for discrete-time planar competitive Kolmogorov systems

DOI10.1080/10236198.2015.1125895zbMath1343.93055OpenAlexW2303124222MaRDI QIDQ2816609

Stephen A. Baigent

Publication date: 25 August 2016

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

Full work available at URL: https://discovery.ucl.ac.uk/id/eprint/1472146/

zbMATH Keywords

invariant manifoldLeslie-Gowercarrying simplexconvexity and concavity

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25) Applications of difference equations (39A60) Numerical methods for difference equations (65Q10)

Related Items

Convex geometry of the carrying simplex for the May-Leonard map, Invariant curves for planar competitive and cooperative maps, On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex, On global dynamics of type-K competitive Kolmogorov differential systems, An augmented phase plane approach for discrete planar maps: introducing next-iterate operators, The property of convex carrying simplices for competitive maps, Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps, A method to derive discrete population models, On existence and uniqueness of a carrying simplex in Kolmogorov differential systems, Chaotic attractors in the four-dimensional Leslie-Gower competition model, Linearization and invariant manifolds on the carrying simplex for competitive maps, TheC¹property of convex carrying simplices for three-dimensional competitive maps, On the dynamics of multi-species Ricker models admitting a carrying simplex, Permanence and universal classification of discrete-time competitive systems via the carrying simplex, On existence and uniqueness of a modified carrying simplex for discrete Kolmogorov systems

Cites Work

• On heteroclinic cycles of competitive maps via carrying simplices
• Competition for fluctuating nutrient
• Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding
• Periodic competitive differential equations and the discrete dynamics of competitive maps
• Competition systems with periodic coefficients: A geometric approach
• The Jacobian matrix and global univalence of mappings
• INVARIANT MANIFOLDS FOR COMPETITIVE DISCRETE SYSTEMS IN THE PLANE
• Fixed point global attractors and repellors in competitive Lotka–Volterra systems
• On existence and uniqueness of the carrying simplex for competitive dynamical systems
• Invariant Curves for Mappings
• Planar competitive and cooperative difference equations
• Some Discrete Competition Models and the Competitive Exclusion Principle^†
• Exclusion and dominance in discrete population models via the carrying simplex
• Ordinary Differential Equations
• Global stability of discrete competition model
• The general properties of dicrete-time competitive dynamical systems