Ann-dimensional competitive Lotka Volterra system is generically determined by the edges of its carrying simplex

2002/10/04 by E. C. Zeeman, E C Zeeman, M L Zeeman +1 · 1 citation
Computer Science · Mathematics · Medicine · #Advanced Differential Equations and Dynamical Systems #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1088/0951-7715/15/6/312

openalex publication_date 2002/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

In an n -dimensional competitive Lotka–Volterra system on R n + the carrying simplex Σ is the invariant ( n −1)-dimensional surface, homeomorphic to the standard unit simplex, that attracts all non-zero orbits and carries the asymptotic dynamics (Hirsch M W 1988 Nonlinearity 1 51–71, Zeeman M L 1993 Dynam. Stab. Sys. 8 189–217). We show that the one-dimensional edges of Σ (as sets) generically determine the system up to multiplication by a scalar, and hence determine Σ and the phase portrait.

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• On existence and uniqueness of the carrying simplex for competitive dynamical systems

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