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A compact invariant set for the Ricker competition model. (English) Zbl 1353.92078

Alsedà i Soler, Lluís (ed.) et al., Difference equations, discrete dynamical systems and applications, ICDEA, Barcelona, Spain, July 23–27, 2012. Proceedings of the 18th international conference. Berlin: Springer (ISBN 978-3-662-52926-3/hbk; 978-3-662-52927-0/ebook). Springer Proceedings in Mathematics & Statistics 180, 127-134 (2016).
Summary: A compact invariant set inside the open first quadrant is constructed for the Ricker competition model (RCM) \[ F(x,y) = \begin{pmatrix} f_1(x,y) \\ f_2(x,y) \end{pmatrix} = \begin{pmatrix} xe^{r-x-by} \\ ye^{\tilde{r} - ax -y} \end{pmatrix} \] under the condition of mutual invasibility.
For the entire collection see [Zbl 1357.39001].

MSC:

92D25 Population dynamics (general)
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References:

[1] Luís, R., Elaydi, S., Oliveira, H.: Stability of a Ricker-type competition model and the competitive exclusion principle. J. Biolog. Dyn. 5, 636–660 (2011) · Zbl 1236.92070 · doi:10.1080/17513758.2011.581764
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