| Abstract: |
| In this talk, we consider a predator-prey model incorporating intraspecific competition in the predator and additive predation on the prey. The additive predation can elicit strong/weak Allee effects in prey, leading to complex dynamics in the model. Our goal is to examine how predator competition affects the species` coexistence.
Analyzing the model with the predator competition coefficient as the bifurcation parameter, we reveal the existence and stability of equilibria, and various bifurcation phenomena such as Hopf, saddle-node, and Bogdanov-Takens bifurcations, as well as heteroclinic and homoclinic bifurcations. These bifurcations identify critical thresholds in the competition coefficient, indicating behavioral transitions. Our findings indicate that the strong Allee effect heightens the extinction risk for both species, but predator intraspecific competition reduces this risk and promotes coexistence. Especially when the ratio of the predator`s mortality to conversion rate is low, there are competition thresholds that trigger a range of initial values conducive to coexistence, which widens as competition intensifies.
Additionally, our analysis shows that reducing the predation pressure on the prey from other potential predators can foster coexistence by inducing a weak Allee effect or eliminating the Allee effect altogether. |
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