Stability Switching in Lotka-Volterra and Ricker-Type Predator-Prey Systems with Arbitrary Step Size

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 to what is 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.

Automated summary

We investigated the dynamical properties of discrete systems under two settings: discrete and continuous. By discretizing time, we obtained stability conditions that maintain the characteristics of continuous models and their numerical approximations. We found that small changes in model parameters can alter system dynamics unless an appropriate time discretization is chosen. We also observed similar dynamical properties in Ricker-type predator-prey systems under certain conditions. Our results highlight the importance of preliminary analysis in determining agreement or disagreement between the dynamical properties of approximated discrete systems and their continuous counterparts.