We consider the Leslie’s prey–predator model with discrete time. This model is given by a nonlinear evolution operator depending on five parameters. We show that this operator has two fixed points and define type of each fixed point depending on the parameters. Finding two invariant sets of the evolution operator, we study the dynamical systems generated by the operator on each invariant set. Depending on the parameters, we classify the dynamics between a predator and a prey of the Leslie’s model.

中文翻译：

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Leslie 在离散时间的猎物 - 捕食者模型

我们考虑具有离散时间的 Leslie 的猎物 - 捕食者模型。该模型由取决于五个参数的非线性演化算子给出。我们证明这个算子有两个固定点，并根据参数定义每个固定点的类型。找到进化算子的两个不变集，研究算子在每个不变集上产生的动力系统。根据参数，我们对 Leslie 模型的捕食者和猎物之间的动态进行分类。