  Dynamical systems are a valuable asset for the study of population dynamics.
On this topic, much has been done since Lotka and Volterra presented the very
first continuous system to understand how the interaction between two species
-- the prey and the predator -- influences the growth of both populations. The
definition of time is crucial and, among options, one can have continuous time
and discrete time. The choice of a method to proceed with the discretization of
a continuous dynamical system is, however, essential, because the qualitative
behavior of the system is expected to be identical in both cases, despite being
two different temporal spaces. In this work, our main goal is to apply two
different discretization methods to the classical Lotka-Volterra dynamical
system: the standard progressive Euler's method and the nonstandard Mickens'
method. Fixed points and their stability are analyzed in both cases, proving
that the first method leads to dynamic inconsistency and numerical instability,
while the second is capable of keeping all the properties of the original
continuous model.
