Geometry of exclusion principles in discrete systems. (English) Zbl 0778.93012

Summary: Using an \(n\)-species system of difference equations with very general density dependent growth functions, we prove that weak dominance and invariance gives the exclusion of all the \((n-2)\)-dominated species in the system. This result is applied to very specific competition models. An example of coexistence in a competition model with no invariance is studied. A notion of strong dominance is developed in a general setting and shown to imply exclusion of the \((n-1)\)-dominated species. An example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given.


93B27 Geometric methods
92D25 Population dynamics (general)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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