一类含时滞的氮–磷–浮游植物模型的动力学分析
Dynamic Analysis of a Nitrogen-Phosphorus-Phytoplankton Model with Delay
DOI: 10.12677/AAM.2022.112088, PDF,    国家自然科学基金支持
作者: 牛凯东：温州大学，浙江 温州
关键词: 营养；浮游植物；时滞；Hopf分支；稳定性；Nutrient； Phytoplankton； Delay； Hopf Bifurcation； Stability
摘要: 本文构建了一类含时滞的氮–磷–浮游植物模型，对模型进行了理论分析和数值模拟。理论分析结果表明，时滞会导致模型正平衡点经由Hopf分支发生失稳，随后我们利用范数和中心流形定理证明了Hopf分支的分支方向及分支周期解的稳定性。数值模拟结果与理论结果一致，且结果表明浮游植物种群密度振幅与时滞参数呈正相关关系。本文结果有助于理解时滞对浮游植物吸收营养过程的影响。
Abstract: In this paper, we propose a nitrogen-phospho-phytoplankton model with time delay and the model is analyzed theoretically and numerically. The theoretical analysis shows that delay can destabilize the stability of the positive equilibrium of the model via Hopf bifurcation. Then we calculate the bifurcation direction of the Hopf bifurcation and the stability of the periodic solution by using norm form and central manifold theorem. The numerical simulation results are consistent with the theoretical analysis, and the results show that the amplitude of phytoplankton population density is positively correlated with the time delay parameters. Our results are helpful to understand the effect of time delay on the process of phytoplankton nutrient uptake.
文章引用：牛凯东. 一类含时滞的氮–磷–浮游植物模型的动力学分析[J]. 应用数学进展, 2022, 11(2): 825-835. https://doi.org/10.12677/AAM.2022.112088

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