An n-dimensional competitive Lotka–Volterra system is generically determined by the edges of its carrying simplex
An n-dimensional competitive Lotka–Volterra system is generically determined by the edges of its carrying simplex
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DOI：
10.1088/0951-7715/15/6/312
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发表时间：
2002-11
期刊：
影响因子：
1.7
通讯作者：
E. C. Zeeman;M. Zeeman
中科院分区：
文献类型：
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作者：
E. C. Zeeman;M. Zeeman
在 Rn+ 上的 n 维竞争性 Lotka-Volterra 系统中，承载单纯形 Σ 是不变的 (n−1) 维表面，与标准单位单纯形同胚，吸引所有非零轨道并承载渐近动力学（Hirsch M W 1988 Nonlinearity 1 51–71，Zeeman ML 1993 Dynam. Stab. Sys. 8 189-217）。我们证明了 Σ 的一维边缘（作为集合）一般决定了系统乘以标量，从而决定了 Σ 和相图。
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.