In this paper, a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten type prey harvesting is investigated. It is shown that the model exhibits several bifurcations of codimension 1 viz. Neimark–Sacker bifurcation, transcritical bifurcation and flip bifurcation on varying one parameter. Bifurcation theory and center manifold theory are used to establish the conditions for the existence of these bifurcations. Moreover, existence of Bogdanov–Takens bifurcation of codimension 2 (i.e. two parameters must be varied for the occurrence of bifurcation) is exhibited. The non-degeneracy conditions are determined for occurrence of Bogdanov–Takens bifurcation. The extensive numerical simulation is performed to demonstrate the analytical findings. The system exhibits periodic solutions including flip bifurcation and Neimark–Sacker bifurcation followed by the wide range of dense chaos.

在本文中，研究了具有米利斯-门腾型猎物收获的改进的莱斯利-高尔捕食者-猎物离散模型。结果表明，该模型显示出余量为1的几个分叉。改变一个参数的Neimark–Sacker分叉，跨临界分叉和翻转分叉。分叉理论和中心流形理论被用来建立这些分叉存在的条件。此外，还显示了Bogdanov–Takens维数2的分支（即，必须为发生分支而改变两个参数）。确定非退化条件是发生Bogdanov–Takens分叉的条件。进行了广泛的数值模拟，以证明分析结果。