Stability of a Delayed Predator-Prey Model for Puma Concolor

TL;DR

This paper develops a delay differential equation model for Puma concolor and its prey, analyzing stability conditions, existence of solutions, and effects of predator-prey removal through numerical simulations.

Contribution

It introduces a new delayed predator-prey model incorporating specific functional responses and stability analysis, with numerical validation of theoretical results.

Findings

Conditions for absolute stability are established.

A unique maximal solution exists and remains non-negative.

Numerical simulations illustrate predator and prey removal effects.

Abstract

This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type function to model intraspecific competition of the pumas. For positive equilibrium, conditions guaranteeing absolute stability are established, based on the delay value and model parameters. The analysis demonstrates the existence of a unique maximal solution for the proposed model, which remains non-negative for nonnegative initial conditions and is well-defined for all $t$ greater than zero. Furthermore, numerical simulations with different parameter values were performed to investigate the effects of systematically removing a percentage of predators or prey. Numerical simulations attempt to exemplify and put into practice the theorems proved in this article.