E C Zeeman and M L Zeeman 2002 Nonlinearity 15 2019 doi:10.1088/0951-7715/15/6/312
E C Zeeman1 and M L Zeeman2,3
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In an n-dimensional competitive Lotka–Volterra system on Rn+ 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.
Issue 6 (November 2002)
Received 14 January 2002, in final form 26 June 2002
Published 4 October 2002
E C Zeeman and M L Zeeman 2002 Nonlinearity 15 2019
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