A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the harvesting as the parameter, we get the existence and stability of the positive steady state, and also investigate the existence of spatially homogeneous and inhomogeneous periodic solutions. Then, by applying the normal form theory and center manifold theorem, we give the stability and direction of Hopf bifurcation from the positive steady state. In addition, we also prove the existence of the Bogdanov–Takens bifurcation. These results reveal that the harvesting and diffusion really affect the spatiotemporal complexity of the system. Finally, numerical simulations are also given to support our theoretical analysis.

中文翻译：

---

带有收获的扩散性浮游植物–浮游植物模型中的分叉分析

本文考虑了具有非线性收获的扩散性浮游植物－浮游植物模型。首先，以收获为参数，得到正稳态的存在性和稳定性，并研究了空间齐次和非齐次周期解的存在性。然后，通过使用正规形式理论和中心流形定理，我们从正稳态给出Hopf分叉的稳定性和方向。此外，我们还证明了Bogdanov–Takens分叉的存在。这些结果表明，收获和扩散确实会影响系统的时空复杂性。最后，还给出了数值模拟以支持我们的理论分析。