## 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.

### MSC:

 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)

strong dominance
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### References:

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