Global dynamics of a Beddington-DeAngelis amensalism system with weak Allee effect on the first species

Abstract

In this paper, a Beddington-DeAngelis amensalism system with weak Allee effect on the first species are introduced and investigated. The existence and stability of all possible trivial, semi-trivial and interior equilibria of the model are studied. By utilizing Sotomayor’s theorem, bifurcation analysis has been proposed and obtain one saddle-node bifurcation. Furthermore, in view of Poincare transformation, the behaviors near infinity and the nonexistence of close orbits are obtained and lead to the presentation of all possible global phase portraits. The global phase portrait in $$R_{5}$$ with two stable node $$E_{2}$$ and $$E_{1}^{*}$$ is a new case due to the appearance of bistable structure. Finally, some numerical examples are offered to verify and extend the analytical results and visualize the interesting phenomenon.