Dynamical analysis of a Lotka Volterra commensalism model with additive Allee effect

Abstract

Abstract We propose and analyze a Lotka-Volterra commensal model with an additive Allee effect in this article. First, we study the existence and local stability of possible equilibria. Second, the conditions for the existence of saddle-node bifurcations and transcritical bifurcations are derived by using Sotomayor’s theorem. Third, we give sufficient conditions for the global stability of the boundary equilibrium and positive equilibrium. Finally, we use numerical simulations to verify the above theoretical results. This study shows that for the weak Allee effect case, the additive Allee effect has a negative effect on the final density of both species, with increasing Allee effect, the densities of both species are decreasing. For the strong Allee effect case, the additive Allee effect is one of the most important factors that leads to the extinction of the second species. The additive Allee effect leads to the complex dynamic behaviors of the system.