Analysis of a May-Holling-Tanner ratio-dependent predator-prey model with an alternative food source for the predator and a strong Allee effect for the prey

Abstract

This paper presents a detailed analysis of a bitrophic chain to understand the complex ecological behaviour applied to this specific model. The model is described by means of a two-dimensional system of ordinary differential equations. The existence and uniqueness of the solutions of this system are examined, as well as their boundedness and positivity. In addition, through a differentiable equivalence, conditions for local and global stability at biologically relevant critical points are established. Periodic solutions are also explored. Finally, the Python programming language is used to perform a quantitative analysis of these critical points, showing different scenarios of the qualitative analysis previously obtained.

Keywords

• Strong Allee effect, alternative food, differential equations, Liapunov function, Chetaev criterion.