In this paper, we consider Bogdanov-Takens bifurcation in two predator-prey systems. It is shown that in the full parameter space, Bogdanov-Talens bifurcation can be codimension $ 2 $, $ 3 $ or $ 4 $. First, the simplest normal form theory is applied to determine the codimension of the systems as well as the unfolding terms. Then, bifurcation analysis is carried out to describe the dynamical behaviour and bifurcation property of the systems around the critical point.

中文翻译：

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捕食者—食饵系统中的Bogdanov-Takens分支

在本文中，我们考虑两个捕食者—食饵系统的Bogdanov-Takens分叉。结果表明，在全参数空间中，Bogdanov-Talens分叉可以是2维，3美元或4美元。首先，将最简单的范式理论应用于确定系统的维数以及展开项。然后，通过分叉分析来描述系统在临界点附近的动力学行为和分叉特性。