Convex geometry of the carrying simplex for the May-Leonard map

DOI10.3934/dcdsb.2018288zbMath1415.37059OpenAlexW2888909737WikidataQ129320762 ScholiaQ129320762MaRDI QIDQ2633645

Stephen A. Baigent

Publication date: 9 May 2019

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018288

zbMATH Keywords

competitive mapcarrying simplexKolmogorov-type mapMay-Leonard map

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Invariant manifolds for ordinary differential equations (34C45) Convex sets in (3) dimensions (including convex surfaces) (52A15) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (7)

On global dynamics of type-K competitive Kolmogorov differential systems ⋮ Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps ⋮ n -dimensional Kolmogorov maps, carrying simplices, and bifurcations at the origin ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems ⋮ Linearization and invariant manifolds on the carrying simplex for competitive maps ⋮ 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

• Unnamed Item
• Unnamed Item
• On heteroclinic cycles of competitive maps via carrying simplices
• On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex
• Carrying simplices in discrete competitive systems and age-structured semelparous popula\-tions
• 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 \(C^ 1\) property of carrying simplices for a class of competitive systems of ODEs
• On invariant hypersurfaces of strongly monotone maps
• Convergence to equilibrium on invariant \(d\)-hypersurfaces for strongly increasing discrete-time semigroups
• On the convexity of the carrying simplex of planar Lotka-Volterra competitive systems.
• Uniqueness and attractivity of the carrying simplex for discrete-time competitive dynamical systems
• On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points
• Curvature formulas for implicit curves and surfaces
• Convexity of the carrying simplex for discrete-time planar competitive Kolmogorov systems
• THE DYNAMICAL BEHAVIOR ON THE CARRYING SIMPLEX OF A THREE-DIMENSIONAL COMPETITIVE SYSTEM: II. HYPERBOLIC STRUCTURE SATURATION
• Convexity-preserving flows of totally competitive planar Lotka–Volterra equations and the geometry of the carrying simplex
• On existence and uniqueness of the carrying simplex for competitive dynamical systems
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Planar competitive and cooperative difference equations
• On smoothness of carrying simplices
• Controlling nonuniqueness of local invariant manifolds.
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems
• A sequential quadratic penalty method for nonlinear semidefinite programming
• Invariant curves for planar competitive and cooperative maps
• Exclusion and dominance in discrete population models via the carrying simplex
• Geometry of carrying simplices of 3-species competitive Lotka–Volterra systems
• The property of convex carrying simplices for competitive maps
• The theorem of the carrying simplex for competitive system defined on the n-rectangle and its application to a three-dimensional system
• Monotone maps: a review

This page was built for publication: Convex geometry of the carrying simplex for the May-Leonard map