In this paper, the dynamics of a phytoplankton–zooplankton system with delay and diffusion are investigated. The positivity and persistence are studied by using the comparison theorem and upper and lower solutions method. The stability of steady states and the existence of local Hopf bifurcation are obtained by analyzing the distribution of eigenvalues. And the global existence of positive periodic solutions is established by using the global Hopf bifurcation result given by Wu [1996]. Finally, some numerical simulations are carried out to illustrate the analytical results.

中文翻译：

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具有延迟和扩散的浮游植物-浮游动物系统中的全局 Hopf 分岔

在本文中，研究了具有延迟和扩散的浮游植物-浮游动物系统的动力学。运用比较定理和上下解法研究了正性和持久性。通过分析特征值的分布，得到稳态的稳定性和局部Hopf分岔的存在。并且利用Wu [1996]给出的全局Hopf分岔结果建立了正周期解的全局存在性。最后，进行了一些数值模拟来说明分析结果。