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

TL;DR

This paper analyzes the complex dynamics of predator-prey models incorporating Allee effects and interspecific competition, revealing various equilibrium stability conditions and bifurcation scenarios.

Contribution

It provides a detailed dynamical analysis of Lotka-Volterra models with Allee effects and interspecific competition, including stability and bifurcation conditions.

Findings

Existence of boundary and internal equilibrium points under various parameters.

Equilibrium points can be stable, unstable, saddle, or cusp points.

Parameter conditions lead to different eigenvalue configurations and bifurcations.

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.