Competitive exclusion through discrete time models. (English) Zbl 1317.92060

Ackleh, Azmy S.; Salceanu, Paul L.

AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 3-21 (2014).

Summary: 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 [the first author et al., Appl. Math. Optim. 51, No. 1, 35–59 (2005; Zbl 1122.35069); Y. Chow and J. Hsieh, J. Difference Equ. Appl. 19, No. 3, 491–506 (2013; Zbl 1328.92058)] to a more general model.
For the entire collection see [Zbl 1297.39001].

MSC:

92D25

Population dynamics (general)

Keywords:

discrete time models; competitive exclusion; common resources; extinction