  Dynamical properties of numerically approximated discrete systems may become
inconsistent with those of the corresponding continuous-time system. We present
a qualitative analysis of the dynamical properties of two species
Lotka-Volterra and Ricker-type predator-prey systems under discrete and
continuous settings. By creating an arbitrary time discretisation, we obtain
stability conditions that preserve the characteristics of continuous-time
models and their numerically approximated systems. Here, we show that even
small changes to some of the model parameters may alter the system dynamics
unless an appropriate time discretisation is chosen to return similar dynamical
behaviour observed in the corresponding continuous-time system. We also found
similar dynamical properties of the Ricker-type predator-prey systems under
certain conditions. Our results demonstrate the need for preliminary analysis
to identify which dynamical properties of approximated discretised systems
agree or disagree with the corresponding continuous-time systems.
