Competition models with Allee effects

Abstract

In this paper, we study a generalized two-species contest-competition model with an Allee effect. We provide a complete analysis of the global dynamics of the system. In particular, we determine all the invariant manifolds, the extinction, the exclusion and the coexistence regions. We use tools from topology and dynamical systems to show that all orbits must converge to one of the equilibrium points of the system. The analysis shows that there are several potential scenarios including competition coexistence, exclusion and extinction.

Keywords::

• Allee effect
• global dynamics
• extinction region
• monotonicity

AMS Subject Classification::

• 39A60
• 92D25

Acknowledgement

This research was supported by a grant from King Abdul-Aziz University.