  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.
