Abstract：
In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.
摘要：
在本文中,我们研究了一个包含营养动态变量的反应扩散模型，浮游植物,和浮游动物.此外，我们考虑了营养吸收后浮游植物生长时间延迟的影响。我们的理论分析表明，时间延迟可以通过Hopf分叉触发模型中持续振荡的出现。我们还分析跟踪了Hopf分岔的方向和分岔周期解的稳定性。我们的模拟结果表明，随着时滞的增加，正平衡会发生稳定性切换。此外，该模型表现出齐次周期2和3解，以及混乱的行为。这些发现表明，浮游植物生长中存在时间延迟会给水生生境的营养浮游生物系统带来动态复杂性。
