<p>This study presents a mathematical model that describes the relationship between the <i>Puma concolor</i> 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 non-negative equilibrium, conditions guaranteeing absolute stability and changes in the stability depending on the delay are established. 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 <i>t</i> greater than zero. Furthermore, a numerical analysis of the stability was developed based on the theorems proved in this article. Finally, numerical simulations with different parameter values are performed to investigate the effects of systematically removing a percentage of predators or prey.</p>