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

Romero-Ordoñez M.A.; Pérez-Núñez J.-R.; Pino-Romero N. · Mathematics in Applied Sciences and Engineering (2024) · DOI: 10.5206/mase/19417

Resumen

This paper presents a detailed analysis of a bitrophic chain to understand the complex ecological behavior 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.

Instituciones: Universidad Peruana Cayetano Heredia; Universidad Nacional Mayor de San Marcos