In this paper, a discrete-time predator–prey model with six parameters is investigated. After splitting the parameter space with respect to the number of fixed points, we obtain both transcritical bifurcation surfaces and a Neimark–Sacker bifurcation surface in the six-dimensional parameter space by the normal form method. Then we apply a hybrid control strategy to control the Neimark–Sacker bifurcation so that the positive fixed point of the controlled system is locally asymptotically stable. Numerical simulations are performed to illustrate our theoretical results.

中文翻译：

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离散捕食－被捕食模型的分叉分析和混合控制

在本文中，研究了具有六个参数的离散时间捕食者－被捕食者模型。在将参数空间相对于不动点的数量进行拆分之后，我们使用标准形式方法在六维参数空间中获得了超临界分叉表面和Neimark-Sacker分叉表面。然后，我们采用混合控制策略来控制Neimark-Sacker分叉，以使受控系统的正定点在局部渐近稳定。进行数值模拟以说明我们的理论结果。