Stability and Bifurcation Analysis of a Commensal Model with Additive Allee Effect and Nonlinear Growth Rate

Abstract

In this paper, a commensal model with additive Allee effect on the first species and nonlinear growth rate on the second species is proposed. The classification, type and stability of all possible equilibria of the system are investigated. We also prove the presence of saddle-node bifurcation and transcritical bifurcation by Sotomayor’s theorem. At the end of this study, an example and its simulations are given to illustrate our main results.