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.

中文翻译：

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连续时间捕食者-捕食者模型的两个离散时间对应物

我们报告了与两个离散时间猎物-捕食者模型相关的数值结果，这些模型是从由两个非线性一阶常微分方程组成的相同连续时间猎物-捕食者模型中获得的。两种离散化都是通过对微分方程组积分得到的，但使用不同的方法。在每种情况下，这种数值结果都与由相关离散化过程产生的二维映射的参数平面有关。然后比较使用这两个图获得的参数平面，我们证明了嵌入在准周期区域中的有组织的周期结构的出现，类似于圆形图的阿诺德舌，这两种情况都得到了验证。