Global attractor and its 1D and 2D structures of Beverton–Holt Ricker competition model

Abstract

Beverton–Holt Ricker competition model is a planar difference system that describes intraspecific competition among individuals and interspecific competition. Known works investigated the stability of equilibria in some cases, showed the existence of stable 2-periodic points when there are no interior equilibria, and found numerically an attractor with riddled basin of attraction for some appropriate parameters. In this paper, we prove the existence of the global attractor, and give a complete description on qualitative properties and bifurcations of all equilibria except for some cases of high degeneracy. Moreover, we obtain different kinds of 1-dimensional or 2-dimensional structures of the global attractor, which were not considered in the known work.