Dynamics of a Predator-Prey Model with Allee Effect and Interspecific Competition

Abstract

This paper primarily discusses the dynamical properties of a class of Lotka-Volterra models featuring the Allee effect and interspecific competition within the predator population. The constructed models employ Holling II and Holling I response functions for the predator, respectively.The existence of boundary equilibrium points under various parameter conditions and internal equilibrium points under specific parameter conditions is discussed. The equilibrium points of the system may be stable or unstable nodes, saddle points, saddle-nodes, or cusp points with a codimension of 2. The parameter conditions under which internal equilibrium points possess one zero eigenvalue and two non-zero eigenvalues, one zero eigenvalue and a pair of purely imaginary eigenvalues, or two zero eigenvalues and one non-zero eigenvalue are analyzed.