Impact of Fear on Searching Efficiency of First Species: A Two Species Lotka–Volterra Competition Model with Weak Allee Effect

In this work, we propose and study a two species Lotka–Volterra competition model, where the first species experiences the mate-finding Allee effect caused by the second species. First, we study the presence and stability of all conceivable positive equilibria and boundary equilibria of this system. Next, by utilizing the Sotomayor theorem, we demonstrate that, given appropriate parameter circumstances, both a saddle-node bifurcation and a transcritical bifurcation exist. Finally, numerical simulations were carried out to validate our theoretical results further. We found that under certain conditions, the system appears to be bistable when the trait-mediated indirect effect is low. However, when the trait-mediated indirect effect is too high, the bistability of the system disappears, and the first species eventually tends to extinction.