On Two Discrete-Time Counterparts of a Continuous-Time Prey-Predator Model

We report numerical results related to two discrete-time prey-predator models, which were obtained from a same continuous-time prey-predator model consisting of two nonlinear first-order ordinary differential equations. Both discretizations were derived by integrating the set of differential equations, but using different methods. Such numerical results are concerned, in each case, with parameter planes of the two-dimensional map resulting from the related discretization process. The parameter planes obtained using both maps are then compared, and we show that the occurrence of organized periodic structures embedded in a quasiperiodic region, similar to the Arnold tongues of the circle map, is verified for the two cases.