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Dynamical properties of numerically approximated discrete systems may becomeinconsistent with those of the corresponding continuous-time system. We presenta qualitative analysis of the dynamical properties of two speciesLotka-Volterra and Ricker-type predator-prey systems under discrete andcontinuous settings. By creating an arbitrary time discretisation, we obtainstability conditions that preserve the characteristics of continuous-timemodels and their numerically approximated systems. Here, we show that evensmall changes to some of the model parameters may alter the system dynamicsunless an appropriate time discretisation is chosen to return similar dynamicalbehaviour observed in the corresponding continuous-time system. We also foundsimilar dynamical properties of the Ricker-type predator-prey systems undercertain conditions. Our results demonstrate the need for preliminary analysisto identify which dynamical properties of approximated discretised systemsagree or disagree with the corresponding continuous-time systems.

Stability switching in Lotka-Volterra and Ricker-type predator-prey systems with arbitrary step size