Competitive Exclusion Through Discrete Time Models
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In biology, the principle of competitive exclusion, largely attributed to the Russian biologist G. F. Gause, states that two species competing for common resources (food, territory etc.) cannot coexist, and that one of the species drives the other to extinction. We make a survey of discrete-time mathematical models that address this issue and point out the main mathematical methods used to prove the occurrence of competitive exclusion in these models. We also offer examples of models in which competitive exclusion fails to take place, or at least it is not the only outcome. Finally, we present an extension of the competitive exclusion results in [1, 5] to a more general model.
KeywordsInterspecific Competition Competitive Exclusion Competition Model Interior Equilibrium Strong Nonlinearity
The work of A.S. Ackleh is partially supported by the National Science Foundation under grant # DMS-1312963. The work of P.L. Salceanu is partially supported by the Louisiana Board of Regents under grant # LEQSF(2012-15)-RD-A-29.
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