In this paper, a deterministic size-dependent phytoplankton–zooplankton (PZ) model with additive Allee effect as well as its stochastic differential equation version is formulated to explore the growth dynamic of phytoplankton. A stability and Hopf bifurcation analysis is performed towards deterministic PZ model, and stochastic dynamic analysis is carried out on the stochastic PZ model, including the stochastic extinction, persistence in mean and the unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulation analysis. Numerical simulations reveal that the synergistic effect of plankton body size and Allee effect can have a complex impact on the growth of phytoplankton in the deterministic and stochastic environments. One of the most interesting findings suggests that the reduced phytoplankton cell size can trigger bistable phenomenon, while the increased phytoplankton cell size or the weakened Allee effect has the ability to destroy such bistable phenomenon.

本文提出了一个具有加性 Allee 效应的确定性大小相关浮游植物-浮游动物（PZ）模型及其随机微分方程版本，以探索浮游植物的生长动态。对确定性PZ模型进行了稳定性和Hopf分岔分析，并对随机PZ模型进行了随机动力学分析，包括随机消光、均值持久性和独特的遍历平稳分布，为数值模拟提供了理论基础。模拟分析。数值模拟表明，浮游植物体型大小和阿利效应的协同效应会对确定性和随机环境中浮游植物的生长产生复杂的影响。最有趣的发现之一表明，浮游植物细胞大小的减少可以引发双稳态现象，而浮游植物细胞大小的增加或Allee效应的减弱则有能力破坏这种双稳态现象。