Convexity-preserving flows of totally competitive planar Lotka–Volterra equations and the geometry of the carrying simplex

DOI10.1017/S0013091510000684zbMath1241.35041MaRDI QIDQ3116818

Stephen A. Baigent

Publication date: 12 February 2012

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

carrying simplexcompetitive dynamicscurvature-preserving flow

Mathematics Subject Classification ID

Attractors (35B41) Invariant manifolds for ordinary differential equations (34C45) Boundary value problems for nonlinear first-order PDEs (35F30) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

Convex geometry of the carrying simplex for the May-Leonard map ⋮ 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 ⋮ The property of convex carrying simplices for competitive maps ⋮ Nonmonotone invariant manifolds in the Nagylaki-Crow model ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems ⋮ The balance simplex in non-competitive 2-species scaled Lotka–Volterra systems ⋮ TheC¹property of convex carrying simplices for three-dimensional competitive maps ⋮ Manifolds of balance in planar ecological systems ⋮ On the dynamics of multi-species Ricker models admitting a carrying simplex

Cites Work

• Uniqueness in the Freedericksz transition with weak anchoring
• Competition systems with periodic coefficients: A geometric approach
• On the convexity of the carrying simplex of planar Lotka-Volterra competitive systems.
• Systems of differential equations which are competitive or cooperative: III. Competing species

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