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

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.

Automated summary

This paper proposes a commensal model with nonlinear growth rate and additive Allee effect on the first and second species, respectively, and investigates the classification, type, and stability of all possible equilibria of the system. The presence of saddle-node bifurcation and transcritical bifurcation is proven by Sotomayor's theorem. An example and simulations are provided at the end to illustrate the main results.