Abstract
In this paper, we study the global dynamics for a Beddington–DeAngelis amensalism model with strong Allee effect on the second species. We treat the maximum value (which per capita reduction rate of the first species) δ as a bifurcation parameter to analyze various possible bifurcations of the system. We analyze the existence and stability of boundary equilibria, positive equilibria and infinite singularity. Additionally, we show that the system under study can not possess global asymptotic stability by the existence of two stable equilibria in the first quadrant. By the existence of all possible equilibria and their stability, saddle connection and the non-existence of close orbits, we derive two conditions for two transcritical bifurcations. Meanwhile, we offer the global phase portraits of this system. Furthermore, we comprise weak Allee effect on the harmed species and offer a new analysis of equilibria and dynamical discussion of the system. Finally, some numerical simulations are offered to support our main theoretical results.
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